No need to concern for your current abilities as everybody had to start somewhere. Your instructor and their assistant have been training for years and that's why they can kick like that.
"i can't do the splits"....neither can I and I can still kick far above my head. Honestly, kicking high is for tournaments and katas (forms), don't get too hanged up on it, even if you're doing TKD, from a self defense point of view, it is impractical most of the time.
With that said, if you are serious about kicking high, I would suggest:
1. FOCUS on every stretch...it's very easy to do half stretches or even start talking to other students, but I don't find it as effective as when you focus on really reaching your maximum and a little more.
2. Give it some time, kicking high and full splits do not come over night, and you are likely to injure yourself if that's what you aim for.
3. Remember that age is just a number. As a culture we've see aging as such a drawback that it limits us everywhere. I would say, turn it around..........so you're 24......that means you've had Twenty Four years of experience to get here, you're much mature, and much knowledgeable on learning techniques and how to discipline yourself to achieve your kicking goal. Use all that to your advantage.
4. Most importantly of all.... ENJOY your training, you'll see progress come along rather quickly actually than if you start to kicking and looking at your calendar every time.
I've only done ITF tkd and teaching style focuses a lot more on the Martial Art aspect rather than the sport aspect. For WTF, it depends on the school, but some focus a lot on the sport aspect since that's what get featured on the Olympics.