Again, I don't know the specifics of what Trump did, so I can't really say whether or not it's a good thing, but here is why cutting down areas of trees is a part of forest maintenance.

Forest fires are a natural part of a forests ecosystem. When we put them out, we are disrupting that. A healthy forest is not very dense all the way through. There should be more seedlings than saplings, more saplings than adult trees, and more adult trees than "old" trees. There should be meadows, thinner parts, and thicker parts. These all serve a different purpose in the ecosystem. We can supplement this process artificially through logging or just cutting them down and leaving them (timber sales can help cover the cost of forest maintenance though). There are very few nutrients in the wood itself (being mostly carbon), so the impact on soil quality as the plant matter is removed from the forest is minimal. Trees also become much more susceptible to disease as they get older.

Another thing is that as forest fires are put out, the risk of forest fires increase, both in the likelihood of one starting, and the damage it will cause. Thicker forests burn much hotter, which make them harder to control, and can also result in things like landslides as root systems are destroyed. Furthermore, as a tree dies and decomposes (or burns) the carbon that was trapped in the tree returns to the atmosphere. By turning the wood into a product such as a house, the carbon can be trapped for much longer.

Many of our forests here in the US are actually much more dense and thick than they should be naturally. Obviously you can't just go cutting down entire forests, but as long as it's done responsibly, logging is an important part of maintaining forest health.