It doesn't sound that bad to me.

I've had a couple of striking coaches that follow the same format. Warm up, combos with pads and then sparring at the end of the lesson. Sparring shouldn't be mandatory but shouldn't be too bad if you tell people you're new (unless you're unlucky enough to be paired with an asshole, which I've experienced).

Obviously the best scenario would be to have someone teach you fundamentals but your weekly classes aren't going to cover that because most people there will already know them. If there's no 'beginners program' or anything along those lines, then you might have to put your hand in your pockets and pay for private lessons.

As for sparring making you better at sparring. He is kind of right. The first time you spar you'll flinch at everything, you can know all the movements and all the combos but still flinch and turn away from punches when put under pressure. By sparring that will eventually go away and you'll be calm enough to work on your technique.