Mixture of licensing, technical, and personality/political/religious issues, I think, depending on the person involved (not everyone has the same motivations). The three big camps are probably: 1. people who think GNU software sucks technically; 2. people who don't like the GPL; and 3. people who really dislike the FSF and/or Richard Stallman.

The first reason probably applies most to big projects like gcc, where it's alleged that the FSF's development process has led to un-modular, hard-to-maintain software. But there are some differences on smaller projects as well, where the BSDs have a tendency to prefer more use of libraries with command-line apps as front-ends to the libs, while the FSF prefers self-contained command-line utilities that interact in the traditional Unix piping style. E.g. GNU tar and GNU gzip are mostly self-contained utilities, while the BSD versions have all the real code in libarchive and zlib, with some command-line frontends.

Some of the more minor rewrites I assume are due to licensing or personality/political issues (I doubt technical reasons are what lay behind OpenBSD writing GNU bc/dc workalikes).