I always wondered this as well when I was a newbie - and nobody could explain it to me in a way that made sense. So, let me give it a shot.
It starts with asking the question of why someone would want to take a line around a race track that isn't the fastest. Seems counter intuitive, right? Well, it all begins to make sense when you sit in the passenger seat of a first timer on track and realize that there is a significant lack of consistency. An earlier than desired turn-in will result in an early apex and more turning to be done when you should be rolling on the throttle and unwinding the wheel - otherwise you'll drive right off the track at exit. The critical piece of difference is that the new driver doesn't know not to roll on the throttle when this happens. Worse, once the new student has driven off the track, their reaction is to usually try to jerk the car back on to the track again which makes a bad situation worse.
Therefore, as a coach, I will recommend a later turn-in for many corners to ensure there is some safety margin to account for a lack of consistency. It's not the fastest, and if you were racing wheel-to-wheel you've opened the door for the person behind you to stuff you on the inside. But in an education environment, it's the safest. In fact, I'm looking for the driver of the car to say, "you're telling me to turn in too early, it's difficult to track-out to the exit curb" --- this tells me they understand the geometry of a corner and the physics related to maximizing the radius of the corner. Until that time, especially if I'm in the passenger seat, I'm perfectly fine with turning in later.
Every corner is different - and like many things in motorsport, there's usually an exception. But the idea is, your coach may be directing you to take a different line that what your racing buddies might be saying - this is for everyone's safety. Take some time to study corner geometry and have a conversation with your coach about why you'd like to try something different.
So, are there other lines?
Of course. There's a Qualifying or Time Trial line which is the fastest. It's not as easy on the equipment and it isn't defensive, but it's what you'll use if you're trying to put down a seriously good lap time.
Then there's the racing (or what I'll dub the defensive) line. Typically, this will cover off a pass under braking (aka dive-bomb) from a competitor. When wheel-to-wheel racing, lap times really don't matter - it's about positions on track. And as some would say, going just fast enough to keep second place from making a move on you.
Then there is the situational line, such as a wet racing line, a line you'll take when there is debris on the track, and various other situations. Just get used to the fact that when someone says the "line" around the track - take it with a grain of salt. And the "student line" is the safe one.