I would argue, that some companies do not want to hire veterans, but there is also a large movement to hire veterans -- but you need to be smart about how you target these companies, and avoid wasting time on the companies which are not interested.
It is very discouraging to apply blindly online -- most online portals are tedious, and generally result in automated responses -- very difficult to get noticed by a robot which performs a key word search when your resume is dominated by military specific accomplishments.
You can supplement your efforts with the shotgun method but don't feel surprised or discouraged when you continue to receive "no thank you responses" for the next several months.
Instead, reach out to actual people... how? ... start with Google... research top companies in your desired geographic location. Search for HR managers (sometimes email addresses will be on company web sites), dominate social media, reach out to specific RallyPoint members who have successfully transitioned, try LinkedIn (they offer free 24 month premium accounts for servicemembers if you email their help desk -- a huge savings) -- enter search criteria such as XYZ company and XYZ military unit -- find someone with common ground with you and shoot them an email -- attach your resume. 90% of the time employees have nothing to lose by passing your resume to an HR representative.... most likely they will even receive a bonus if you are hired.
Be friendly and dress the part. Networking happens in real life too. Strike up conversations at bars, on airplanes, at the gym - you never know. Work on your pitch, seem enthusiastic about the transition -- even if you left the military for negative reasons.. always speak positively about what you learned and gained and now have to offer a new company.
Tailor your resume... don't be lazy about it. Let more than one person review it and offer recommendations. Resume writing is also discouraging because EVERYONE has a different opinion about what you should or should not say... but it takes work to present yourself well. Cut out the military jargon, translate your accomplishments into something that a civilian employer would understand, and tailor each resume draft to whichever specific job you are applying for. There is no point in applying if you are too lazy to tailor your resume for a position. Emphasize traits which are specific to the position.... EXAMPLE... if you are applying for a job focusing in engineering.... you may not have an engeering degree... but you may still be able to write... "undergraduate studies included Electrical Engineering, Mechanical Engineering and Calculus I-III" ... also, don't be the guy who says,... I already let so-and-so review my resume... don't assume that means it is good. Most of the time when I review a resume, it takes me 2-3 versions to eliminate the glaring mistakes and start to critically think about ways to refine the resume.
1. Talk to actual people, waste less time filling out online applications.
2. Don't be lazy with your resume, it matters.
3. Don't get discouraged, "hiring veterans" is definitely "in" right now -- just not all companies are on the same page, just change your approach in order to find the companies that are seeking vets.