A: Some engineers feel that equalizers sound different when you cut with them, versus boosting with them. And, in some cases, there may be technical reasons why this is true.
But, for many engineers, another big reason is to preserve headroom. Adding a boost to a set of frequencies can take a big chunk out of the available headroom. Often you’ll get better results by cutting frequencies, then you’ll have room for dynamic peaks, and also possibly be able to turn the overall level of the signal up, since you’ve preserved headroom.