Why does the army force good soldiers away from re-enlistment?

I've reenlisted probably over a thousand Soldiers by now and I would very much disagree with that statement. Young Soldiers like yourself are very emotionally driven. If you ask a group of first term Soldiers if they plan to reenlist, they'll all tell you no. But 80-90% of them who are eligible to reenlist, will.
On one day, they will walk in and swear they're never going to reenlist. A few days later, their buddies will tell them about this magical place - Campbell, Bragg, Europe, USASOC - where everything is better and they get to deploy, and they'll reenlist for it. Then two weeks later they'll have a bad day and ask if they can get out of their contract. A month after that, they can't wait to leave. After getting to their new duty station they realized how much they miss the last one.
It's all just a bunch of emotions until you start treating it like a career instead of a life adventure.

As for getting driven so hard, the ones who work are the ones who get promoted. Bare minimum you have to make E6 to stay in long enough to retire. But you're an 88M, you can realistically retire as an E8 in 20 years. Those Soldiers who do the minimum, get the minimum. Those who work hard get the choice assignments that get them promoted. They get selected for schools that translate into post-retirement certifications like Project Management, Lean Six Sigma, and others.

Spend less time worrying about others and focus on your own growth and you will be happier.

Absolutely. It's a major problem. That's why we have other opportunities that only quality Soldiers qualify for. CMFs 18/37/38, 160th, 75th RR, SMUs, Attache, WHCA, WHTA, JCU, OSW, JSOC. (list does NOT include SFAB)
Drop packet, leave conventional where shammers sham and quality is run down.

My experience in the public and private sectors say people do not leave companies (organizations), they leave managers (NCOs and Officers). Everybody in a supervisory or leadership position is mutually responsible when a Soldier decides not to re-enlist. In some cases it's a good thing. You don't want the POS Soldiers re-enlisting. You do want the hardworking, dedicated, honest Soldiers to re-enlist and get promoted. I wholeheartedly encourage leaders to set standards for excellence and hold their Soldiers and Civilians accountable for meeting those standards. Those who violate directives must be rehabilitated if possible, but "chaptered" if not. Disciplinary actions, including USMJ Article 15, can be part of rehabilitating a Soldier or part of getting them out of the Service. In addition, publicly praise and award the Soldiers who positively exceed standards.