How is it that the Army is recruiting but downsizing?

Without recruiting we as leaders will run out of soldiers to lead. A large portion of junior enlisted are one timers.

Because every years, thousands leave the Army due to ETS or retirement. We need to make sure they are replaced so we can maintain somewhat of a steady state. The Army has to look long range also to make sure there will be enough senior NCOs and officers down the road as far as we can see. There are statistics to show how many new Soldiers we need each year to have X number of CSMs 25 years from now. Now what you may see is a reduced recruitment mission as I see that for officers in my role as a Recruiting Operations Officer for an Army ROTC program.

You just raise standards i.e. Entry scores, high school graduate, no criminal records, etc. quality not quantity.

A lot of others have made the point but to answer your question, downsizing is necessary to reduce leaders at the higher levels especially that are no longer necessary. Individuals who don't progress are wasting army time and money. Recruitment however won't change because of budgeting requirements.
As an example a specialist with 8 years makes $2461 per month. A private brand new makes $1546. So if the army releases the specialist from service, it can acquire a New soldier and save over $900. Multiply that by a force reduction of 40,000 troops the Army saves 432 million dollars per year.

It is about the needs of the Army.

With a new soldier, it is understood that there is training time, slots to fill, etc. They are recruited to jobs that need filled at the junior enlisted level, which are usually plentiful.

The NCO ranks have always been filled by promotion, rather than recruiting.

With a prior service soldier that has had a break in service, it is a little different. There are fewer NCO roles the higher you go. Those NCOs that have made that rank are more likely to stay in than get out. Your skills may or may not meet the rank and MOS needs of the Army. Depending on the length of the break in service, there are also training requirements for the prior service NCO as well. The Army doesn't necessarily budget for that in recruiting and training. How much have regulations changed in even the last couple of years? For example, it can be quite difficult for an NCO who is expected to enforce AR 670-1 when all of the uniforms are different and the rules have changed.

Every Organization you always need fresh blood and it is more important in the Military. Can't have SSGs without Troops to Supervise. They are just going to have fewer at each level.

Without a doubt we have to account for natural attrition. So recruiting will continue. People who make a lot of money come up with how many we bring in based off what we need to lose.

Privates can't stay privates forever. I don't think we will be taking the numbers of the past but we are losing people everyday due to completing their contracts. You have to keep the new soldiers coming in to replace those that are left.

Approximately 300,000 service members leave the military every year. We are still engaged at a different capacity in other countries, and the Army, like other branches, have to find the talent of today to defend our tomorrow - just a thought from my end.

Overall population is a small part of the equation. It's about having X amount of people at Y rank in B MOS at any given moment...

There will always be shortages and over strength MOS's. They recruit the shortages, what they are doing is trimming the fat from the middle.

They are reducing units and positions. They still need people to replace the large number of Soldiers that ETS normally.

Privates are cheaper than SSGs. They are less opinionated and more PC. They aren't thinking about retirement any time soon

The Army always needs more Privates.
Always.
Even when it is shrinking.
They are the muscle that makes a unit go.

Well they have to still recruit new soldiers to replace the ones we loose to war and to ETS. Plus you have to look at the ones who are retiring and the lower ranks who don't make the rank and the allotted amount of years. It's harder to get into the military now. I've talk to a few of the young adults who are getting ready to graduate school and it's allot harder on them to come in. If you have been on a ADHD medicine or have bad asthma and have been on medication for that also you have to wait or prove you no longer have it. They want perfectly healthy recruits now. My son couldn't get in because of asthma and ADHD medication and my daughter also. I also have one young man I'm mentoring who was on the medication for ADHD and they told him he need to wait a year and be off the meds for a year before they would look at him. You know the use to just say children had ADHD in the ninetys when they couldn't figure what was wrong with them.

forced retirement, PT failures severed from service, MOS shuffle and general reorganization process and house cleaning and promotions and of course new cruits being brought in all to fill in the gaps.
But mainly its the MOS and soldier shuffle downsizing in certain areas and increasing in more vital areas that are running short.

To me it seems like they are bringing in Soldiers just so they can QMP or QSP Soldiers. Then we will have the problem of promoting Soldiers into the NCO Corp that do not know what they are doing and the Army is going to be really in a bad spot.

It has to do with maintaining a year group population. Prior service upsets the balance. That and the prior service folks left for a reason, easy street is not all that easy is it.

This is a good question. I have pondered this as well. Troops are lost to attrition, combat (wounded or KIA) and disability all the time. I would hope that recruiting occurs at a rate equal to or higher than attrition. I also think that once Obama is no longer President, downsizing of the military will be put on a back burner until the multiple conflicts we are involved in are ended. I am all for saving money that is handed out abusively to contractors and support entities.

Some of these answers are really amazing. Rather than state again some of the actual answers, there is a Brookings Study that addresses this process to great detail supported by input from Odierno. Look up "getting-active-army-end-strength-right-evans/army-end-strength". It addresses the point of where the remaining 450,000 remaining troops will be assigned and the flaws with the adding of junior personnel, while letting career depart. OK, one paragraph:

Based largely on the historical elasticity of the Army, many believe that a relatively small
force can be maintained and then rapidly expanded during times of national need. While
the draft allowed for this type of expansion during the 19th and most of the 20th century,
the advent of the all-volunteer force presents challenges to this technique. The speed of
innovation and information technology has increased the pace of operations and the
ability of malign actors to spread effects, influence, and actions across the battlefield.
The ability to rapidly deliver trained and ready combat units is essential to the 21st
century Army. Most soldiers in the Army today spend at least five years in the service.
This amount of time is essential for them to develop reasonable expertise in
increasingly difficult military skill sets. By contrast, draftees of the past spent only two
years in the service, far less time than required to develop even a modicum of expertise
on the complex battlefield systems and network modalities of the 21st century.
Additionally, disparities of race and ethnicity would be skewed by a draftee force,
amplifying the challenge to maintain diversity in the Army and keeping it a force that
provides a representative sampling of the broader American population