I think by "better programmer", he meant you will function better as someone who writes code in the context of a team. And using branches properly can (a) help other people grok the code you write, (b) help you maintain clarity with an influx of change requests.

Of course advice to "just use branches" is not going to make up for core deficits in your programming knowledge. But in my experience a lot of the trouble we get into on software teams is due to workflow problems and misunderstandings rather than "bad programming".