Why is it hard to be a young boss?

It does get better with age. When you are in a position of authority at a young age, there are always going to be people who perceive that you may not know what you are talking about because you lack experience. It’s like the attitude is “I’ve been doing this for 15 years, who is this kid to come in and tell me what to do?”. And you will probably spend some time having to justify (through your actions and performance, not with words) that you are actually qualified for your job and know what you’re doing/talking about. Yes, it can be frustrating, but it if you stay in the same company for a while, people will learn that you know your stuff. If you bounce around a little, you will likely encounter similar everywhere you go, at least until you get a bit older.

Although I'm semi-retired now, I had the same problem when I was your age.  Its something that will fix itself as you get older. For now, I would recommend 3 things. (1) Try to resist the urge to come down in a heavy handed way in order to put a quick end to debates from subordinates.  Learn some techniques such as, "I understand your concerns, but we need to get this work done.  We just don't have time to discuss it now." (2) When you are older, remember how this lack of respect irritated you.  Be sure to support the next young manager.  (3) Be careful to know the difference between subordinates arguing with you, and giving honest suggestions. 

I would add that, depending on what line of work you are in, your age can also work against you with customers.  In the accounting profession, for example, no clients want to be assigned to someone who is young.  That will pass as well.

I don't know, I was not a boss after 24. Nobody questioned or challenged me. Might be in your head.