How is it that the Army is recruiting but downsizing?

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