Yes, some students enjoy writing proofs. They accept the task as a challenging puzzle, one that provides an agreeable sense of completion once you’ve successfully threaded a path from the given information to the conclusion.
I was one of those students. But we were — and are — in the minority. The majority of students find proof-writing difficult, inscrutable, and not very interesting. Worse yet, they find it pointless. This may be especially true when the artificial strictures of two-column proofs are imposed.
One remedy for teachers and learners alike is to read two engaging essays: “What Is Mathematics For?” by Underwood Dudley, and “Why do we have to learn proofs!?” by Joshua N. Cooper. Both of these make it very clear that the current trend of justifying math by its practical, sometimes even career-oriented, real-life applications is misleading at best and dishonest at worst. The major reason to learn algebra, proofs, and other parts of mathematics is that they teach you to become a critical thinker. I admit that math isn’t always taught that way, but it should be. Treating a proof as a puzzle isn’t dumbing it down, it’s the essence of logical thinking.
More on this later. In the meantime, read the two essays!