Why was Civil War billed as a Captain America movie as opposed to an Avengers movie?

You are certainly right that this film seems to be chock full of Avengers. However, it is still a rather personal Captain America movie through and through. You could as well ask that question about Natasha Romanoff, the Black Widow, in Captain America: The Winter Soldier. It's about more than just screen time.

While there is a larger conflict between the two parties in the Avengers arising due to the UN act on limiting their individuality, the thing that makes it escalate is actually Steve's friendship to Bucky, the Winter Soldier, and his tries to help him and handle the matter personally, against his fellow Avengers and the new established laws. Captain America is the primary driver behind the opposition in that film and he only is because of his personal matters. While Captain America refused to sign the UN law, he was still smart enough to not go downright postal against the law enforcement and his Avengers colleagues, not until he has a personal reason for doing so. If it weren't for his friend Bucky, he'd just sit around abiding the new UN law, even if under protest.

This is still a rather personal Steve-story embedded into the admittedly larger conflict about responsibility that touches all the MCU heroes. Even Tony, who turns out to be quite personally involved in the matter himself is not so much until the very end.

While marginally referencing the larger events at the end of Avengers: Age of Ultron and employing characters introduced therein, the movie is primarily a direct (and thematic) continuation of Captain America: The Winter Soldier, concentrating on the eponymous character introduced in that, and his friendship to Steve Rogers introduced in Captain America: The First Avenger, together with a variety of other minor characters only known from the previous movie, like Sharon Carter or Brock Rumlow (Crossbones).

As expained in this excellent answer by @phantom42 on SF/F, Kevin Feige (the head of Marvel's film studio division) discussed this point last year, when talking about the number of characters in the movie. The basic explanation is that, while many of the Avengers are in Civil War, only a few characters get a real story-arc, and all of those are related to Steve Rogers development as a character:

"There were a lot of characters in The Winter Soldier, but it felt like a very singular and relatively simple thriller. Civil War follows in that same way," Feige said. "I think that's something [directors Joe and Anthony Russo] pride themselves on, and our screenwriters Chris Markus and Steve McFeely are excellent at giving each character just enough. They're not full arcs for everybody; it's just enough that their presence is felt and important, but that the very clear single story that is being told is being served at all times."

In addition, the central plot of the movie is not the Avengers fighting against a bad guy to save the world. The movie is about Captain America fighting to prove his friend innocent. The other characters are minor, guest, or even cameo appearances, which serve to tie the movie into the larger Cinematic Universe, but they aren't integral to the plot.

In particular, note that

in the final act, where the climactic battle and resolution happens, it's down to just Steve Rogers, Bucky Barnes, and Tony Stark.