I had the same problem when I was in high school. No one could understand why I couldn't just DO it. Now I'm 23 and have never performed a bhs outside of the practice gym.
As a coach, I've had the opportunity to run a cheer tumbling class for a gymnastics facility. They taught me so much about conditioning properly for each skill leading up to a bhs and beyond. I even learned why I had the same problem you're having.
You may not be trained enough with the RIGHT muscles to perform your bhs safely. Sure, you can support yourself on your arms and you have the power to throw yourself over, but it may not be enough to reduce the risk of injury.
My advice is to perfect the basics. Continue working on your bhs, but constantly be perfecting your handstand, cartwheel, roundoff, etc. The more correct your basic skills are, the easier your advanced skills will come. The handstand drills on this site are great, and (I haven't checked) they may have drills for cartwheels and roundoffs too. Remember it's not just about being able to throw yourself over or kick your legs up. It's about using the RIGHT muscles to control each skill, so find some gymnast-proven drills for the basics and beyond. I'd be happy to share some too, just send a message.
Good luck!