Lots of good advice here already, but I don't see a lot that addresses your title question:
How to figure out why parents are so strict about Internet access?
Several answers reference "inappropriate content" or "garbage", and a couple directly reference porn as an example of content your parents may want to protect you from, but that's not a very thorough explanation. I'll try to add a little more context for you.
Generally speaking, there are two ways in which internet access can be dangerous: you can get access to people or material that can do you harm, and you can share aspects of your own life that can do you harm either immediately or down the road.
Accessing dangerous people or material
What counts as dangerous is highly subjective --- you may want to open a conversation with your parents about what kinds of things they're afraid of you encountering.
There is a lot of content on the internet that many people would not want their children to access. Some examples: porn (some of which glorifies highly sexist, racist, or violent tendencies), pro-eating disorder websites, extreme political content, stupid/dangerous "advice" about health and nutrition, stupid/dangerous "advice" about sex and relationships, etc.
In all of these cases, the concern is that reading or viewing this content will influence the way you think about the world --- and believe me, it will. I don't mean that reading one racist blog post is going to instantly turn you into a bigot, but rather that the environment you put yourself in shapes you. That's true for everybody. Your parents know that, and they're trying to ensure that the environment you put yourself in is one that will support you growing into a good, healthy person.
In addition to the danger of having your worldview shaped by a lot of the baser elements of human nature, there's another kind of dangerous content: people trying to get you to do something dangerous. There are people who want your money, want your identity, or want you to do things for them. One extreme example is sex trafficking: US minors who get trafficked often meet and communicate with their trafficker online, and this trend is increasing. Another example is scams, some of which can fool even very savvy and careful people.
In some cases, it's actually your parents who would be on the hook for your actions, so it's really pretty reasonable for them to restrict your ability to do that kind of damage (I had a friend in high school who downloaded some music files illegally in a way that she thought was safe, something went wrong and her family ended up getting sued for a quarter of a million dollars by the copyright holders, no joke).
Important thing to keep in mind: Are the people generating this dangerous content or coercing dangerous actions stupid, artless trolls? Some of them are, but many are not. There are some sophisticated, smart people who make a living tricking and manipulating others online, and they are very good at it. You'll certainly see blunt, laughable malicious content online, but that's probably not your parents' major concern; the clever, subtle stuff is much scarier.
Sharing aspects of your own life that can do you harm
Everybody makes mistakes, especially teens and young adults, even very responsible, level-headed ones. It's part of growing up. Your parents expect you to make mistakes (and you should, too). A problem can arise, though, if your mistakes become permenantly available by being shared online.
Good kids --- who grow into kind, thoughtful adults --- often think or say things they later regret (sometimes in an attempt to be edgy or funny). Things like racism, rape, or disability can seem funny before you grow up enough to understand how very real they are. Another thing to consider is that your own perspective will shift over time, and even what feel like genuine, strongly-held beliefs now may turn out later to moderate or disappear altogether. Saying things you later regret is part of growing up. If you put it in writing, though, and share it online, it can come back to bite you.
Another more extreme example of sharing material that can harm you is sexting, but even more benign behavior can come back to haunt you if it reaches an audience you didn't intend.
The important thing here is that people interacting online are much more accountable for what they say and do, over a much longer time period. Your parents doing things that push your interactions into "real life" instead of online may be an attempt to let you make your mistakes where they can be fleeting.