I'm going to be blunt: this is an internship that only lasts a few months; the person hiring you doesn't expect you to accomplish anything important, doesn't care about your skills (apart from being able to perform the task you're being hired to work on) and probably wants as little interaction with you as possible.
That might sound really mean. But you have to understand what this dynamic looks like from the rest of the group. You're coming in, and we know you're only going to be here for 10 weeks. That's not enough time to train you in enough of the company's internals for you to be solving any critical problems. And, well, why would we want you to waste a significant portion of your time learning those internals? That knowledge is leaving the company in 10 weeks and becomes worthless. Likewise, why would we want to have a regular employee spend their time up-skilling you? That's not only cost even more salary, but we'd also be losing the regular employee's productivity during the time they train you.
Instead, it's very important to understand why you're there - because that understanding will make a world of difference on whether you're successful during your internship. You're there to do low-oversight/low-training work so that the regular employees can focus on the important stuff. You're there to 'free up' people.
If you want to have a good internship? Then you should work as hard as you can to maximize one specific ratio: Value delivered to the company divided by Time spent supervising/assisting/training you. (By the way, this ratio is a good thing to at least be mindful of when you're a Junior as well - sometimes 'bringing the new guy up to speed' poses a pretty bad efficiency hit and trying to mitigate that a bit can be very appreciated; one of the reasons I was loved starting out fresh from college is because I could be given a relatively unimportant project, run with it without a whole lot of supervision, and deliver a relatively decent end product.)
Now, if you reread what the manager is saying, it might make a bit more sense. Granted, it's still got a bit of a rude tenor to it, but it starts to seem a bit less random (they don't care about your prior skills if those skills won't help you accomplish the specific tasks they have for you; they probably don't care all that much what specific methodologies you use to accomplish your tasks as long as they're done correctly; they don't want to spend a large amount of time in interaction with you, etc.) This is why I don't think you should quit the internship - while some places might have a softer edge to them, ultimately you're just there to free up the full-timers to focus on more important things.
Finally, some bits of advice during the internship:
- Be as diligent as possible. Aim for 0 mistakes. Even if it means
taking longer to accomplish your tasks - because the less
oversight/correction needed from the regular employees, the more
you're helping the team focus on their regular tasks.
- Try to get as concrete of a picture on what you're doing up-front.
And after you figure out how you're going to do something, jot off an
email to your supervisor along the lines of "I think I'm going to X
and Y in order to get Z, and then I'll put it all together with W."
This gives your supervisor a quick way of correcting any bad path you
might find yourself going down.
- Try to deliver preliminary/mock results as quickly as possible - aka,
Fail Quickly. "I've made a mockup of M and N - does it look good?
Should I flesh it out, or does it need to be tweaked?"