I work in an office thats taken over 2 years (and still counting) to move to a Git/Branch workflow model from an RCS based config management tool. i.e. Git with gerrit was installed 2 years ago, yet releases and half the team still use the old tool. The old tool was a state of the art configuration management tool in 1994, and has features that Git/Gerrit do not provide, but branch based revision control is not its strength and manual copy/paste is how branches are managed.
The guys who have used this tool for 20 years have no awareness of the benefits of properly managed branches and merging, and strongly believe if you do not make every source change by typing it in yourself at a keyboard it cannot possibly be correct.
Another problem with branches also happens when code branches diverge to the point that they are no longer the same code base. This often happens in the above scenario as keeping everthing in sync is hard - if a change is not needed in one repo, the manual effort to merge it is seen as a waste of time. Do this a few times over a few years, and automatic merging becomes more difficult to manage than manual merging.
Some simple things for a person to resolve are impossible to automate. As the merges were not automated, no understanding or disipline exists around these things, and automatic branch merging usually fails. A couple of difficult merge conflicts reinforces the mindset that its not reliable. Code layout changes are a really good example, as are changing tabs to white space and training white space changes in files - things a person does not see or care about, that stop a merge dead in its tracks. Refactoring while making a one line defect fix, or worse - doing multiple unrelated changes in one commit - its easy for a person to tell which bits are needed, but a merge tool cannot.
No amount of technical training or refering to current best practice will change their belief system. Until they move over and start using branching, they will not be comfortable with it. Hence a catch 22. They won't move because the are not confident in it, they won't become confident until the move.
Putting it bluntly, most of the circumstances that branches are considered harmful is when dinasours who are not prepared to change and have never used it are in control.