I've self-taught, gone to college, apprenticed, and taught others. I don't think we have enough information to determine the teachers motivations, but let's assume this teacher just wants to see you excel and is trying to guide you based on their experience.
The question will eventually boil down to what you want to do with your art. If you just want to draw what you like you certainly don't need to accrue massive debt to do so, there are plenty of ways to learn. Certainly many of us started drawing because it made us happy and for many, that is enough.
If you want to earn a living doing commercial art in advertising or animation or other careers, school can be a benefit. But, whether you are at an agency, in an animation bullpen, drawing comic book pages, or just working freelance, very often you will be asked to draw in someone else's style. So having a broad pallet to draw from is an asset. But this doesn't mean you can't develop your own. This may be what your teacher is encouraging you to pursue.
From my own experience, I often felt a similar way about the style I drew in. But the truth was (and this may not be you), I lacked confidence that I could do anything else or I just dreaded the feeling of starting all over again. However, when I was pushed to expand my skill set, it had a profoundly positive effect on my own style. Sometimes we all need a friendly nudge.
That said, schools have pitfalls... crippling debt being foremost. There are rubber-stamp schools where every one gets a passing grade if their tuition is paid on time, regardless of their skill. There are teachers who don't teach because they perceive their students as competition. There are teachers who have skill, but don't know how (or have the patience) to share their knowledge. There are teachers who only produce clones because they never pushed themselves out of their comfort-zone. And the big con... Artsy-Fartsy. Those are schools/teachers that expound on art as some nebulous, magical, undefinable thing that can't truly be taught... that's total BS.
The only thing that can't be taught, is the desire to learn.