I personally think majoring in philosophy (including studying it at a graduate school) has helped me improve my writing skills. I use to be a terrible writer (and I still have a huge room for improvement), but I learned how to write more clearly and precisely than before. I also learned how to summarize someone's argument concisely and accurately. What really helped me was that there were professors who cared enough to provide me constructive feedback that I can use to improve myself.

Nonetheless, I do think that I learned more philosophy outside of class from reading Stanford Encyclopedia of Philosophy and philosophy books/articles in my spare time. Philosophy courses
provide you philosophy articles/excerpts that you can discuss in class, but you can easily access them on your own with your school account. Even if you don't have access, you can easily find a lot of philosophy papers uploaded by a professor in his/her own website for fair use.

I would also add that reading philosophy books written for both students and professional philosophers is what really helped me to learn philosophy. For example, Jaegwon Kim's textbook on Philosophy of Mind was written for both students and professional philosophers. In his textbook, he usually tries to represent arguments in their syllogistic form to help us see whether or not it is valid and sound. Moreover, he shows various of ways to "attack" the argument such as arguing that one of the premises is false or one of the premises is making an unwarranted assumption and so on. This helps you learn how argumentation works in philosophy and as you read more you'll eventually pick up pretty fast.

"How do the solutions where you actually change tracks deal with the scenario of the fat man? The scenario where you can throw a fat man off the bridge to stop the trolley hitting five workers." — Purple Pond

Consequentialism would say that pushing the fat man is morally permissible since it yields the best consequence (e.g. saving more people). However, the Doctrine of Doing vs. Allowing, Doctrine of Double Effect, Positive vs. Negative Duties, and Foot's distinction between initiating vs. redirecting causal sequence would all say that it's morally impermissible.

Since the Doctrine of Doings vs. Allowing states that doing harm is worse than allowing harm, pushing the fat man counts as doing harm and thereby it is morally impermissible. Doctrine of Double Effect states that if the intended goal constitutes harm (e.g. pushing the fat man in order to stop the trolley), then it is morally impermissible. Since your goal is to stop the trolley by pushing the fat man, it is morally impermissible. The view that negative duties trump positive duties would say that pushing the fat man violates a negative duty, so it is morally impermissible. Foot's distinction between initiating vs redirecting causal sequence would say that since pushing the fat man is initiating a causal sequence (e.g. pushing him leads to his death), it is morally impermissible.

It's worth to consider different competing views on what you ought to do in the Trolley case. One view states that you should pull the trolley because it leads to the best consequence (e.g. maximal happiness). This is the consequentialist view. Second view is the Doctrine of Doing and Allowing which states that doing harm is worse than allowing harm, so you don't pull the lever.

Third view is the Doctrine of Double Effect, so you intend to save three people, but the death of one person is simply a side effect of your action of pulling the lever. According to this view, as long as your intended goal is to save people rather than to kill people, it is morally permissible.There's another view by Foot which states that negative duties (e.g. you ought not to kill) trump positive duties (e.g. you ought to help the poor), so since pulling the lever would violate your negative duties you shouldn't pull it. There's also this view that it's morally permissible to pull the lever because you aren't initiating a chain of events, but rather redirecting it.

There are many other different (and equally important) views, but the above ones are ones I can think on top of my head.