I have a couple reasons

It's a good excuse to be outside either alone with friends, get a little fresh air and sunshine, enjoy nature, etc. it often doesn't involve the same sort of investment or level of physical fitness that, say, hiking does. It can be damn close to doing nothing, but it's enough of a thing that you don't feel guilty for doing nothing all day. The initial cost investment can be pretty low, you can probably get out and go fishing with less than $50 worth of gear from Walmart, and ongoing expenses are pretty low too, a couple buck every trip or could trips for bait, and a couple more bucks here or there for some extra bits of tackle.

You can put as much or as little time, money, or effort into it as you want. A $20 Walmart rod catches fish just fine, or you can spend hundreds or probably even thousands of dollars on a rod that also catches fish just fine. You can go out once or twice a year when the weather is nice, or you can be out damn near every day, rain or shine. You can learn a lot of different techniques, use different baits, lures, rigs, etc. to catch more/bigger/different kinds of fish, or you can have a worm on a hook at the end of your line that you just throw out in the water and let whatever's gonna bite bite. There's skills to learn if you want to, or you can coast by on just luck, sometimes the fish just aren't biting, sometimes they'll bite anything you put in front of them.

And because of that, fishing is kind of a great equalizer, you will meet all kinds of people out on the water or in the fishing aisle at Walmart, people of all races and classes fish.The techniques, targeted species, equipment, locations, etc. may all vary, but at the end of the day we're all out there trying to outsmart fish and coming up empty-handed as often as not. If you meet someone else who is a fisherman, you've got common ground and something to talk about even if you have nothing else in common. We all love to talk fishing, trade fish stories, share our tips and tricks, ask people we see fishing as we walk by how they're biting, etc.

There's also a meditative aspect to it for sure, repetitive motions, silence, solitude, nature, a certain amount of mindfulness, etc.

Fish are cool, and catching them is a good way to get an up-close look at them.

There's a lot to be said about being connected to where your food comes from, the environmental impact of commercial fishing, the health benefits of eating fish, the cost of buying or catching fish, etc. that frankly could probably be the topic of several whole books, and I'm not going to go into all of that, and just kind of leave it at fish are food, and catching fish yourself is one way to get food, and it comes with its benefits and drawbacks.

As for the weather, I'm a strong believer that there's no such thing as bad weather, only inappropriate gear. With enough of the right kind of layers, you can be perfectly comfortable. Sometimes it's nice to be out experiencing that, it's a side of the world you may not often see or take the time to appreciate. For some fish, that weather may be ideal for catching them. Some people can't or won't brave the elements, so the places you go may be less crowded, which is nice if you're seeking solitude.