To understand this phenomenon, you need to know something about the culture of sports in the US.
First: there is no promotion/relegation system for professional sports. This means that in any particular sport, most of the US has no local professional team at the highest level. And if you are not living near a major metropolis, you are not likely to ever get one. There are 32 NFL teams with no expansion on the horizon.
Conversely, there are 128 teams at the top level of NCAA football (Football Bowl Subdivision). Over 97% of the population1 lives in a state with at least one school which plays at the FBS level. This gives nearly everyone in the US some kind of local team to root for. (And unlike NFL games, it's actually affordable to go to a college game.)
Second: NFL teams are not a constant. College teams are. NFL franchises, unlike European football clubs, are not tied to a city. Just in the last two years, three different franchises either moved (St. Louis Rams to Los Angeles, San Diego Chargers to Los Angeles) or announced plans to move (Oakland Raiders to Las Vegas). Or look at Baltimore: the old Baltimore Colts won three NFL championships and a Super Bowl, then moved to Indianapolis and won another Super Bowl. The Cleveland Browns moved to Baltimore, changed their name to the Ravens, and won a couple of Super Bowls; meanwhile, a new Cleveland Browns team was formed to replace them.
Colleges don't do that. If you live in Alabama and your grandpa's grandpa lived in Alabama, you're still rooting for the same school that he did. Or maybe you did switch from Alabama to Auburn (or vice versa), and that could cause tension at family gatherings for years because the rest of your family is still loyal. This happens all over the country, but most particularly in the South (source: anecdotal).
It is also important to note that perhaps none of you actually went to the school that you cheer for. You may have gone to another major school, a small school, or no college at all. College attendance is not a prerequisite to college fandom.
Third: College sports predated professional sports by decades. I touched on this in the last point. College sports are more established, though the NFL has better television deals now. People grew up watching their team.
All of that is to tell you this: in large swaths of the United States, people watch the NFL -- but they care about college football.
I personally know people who root for a particular NFL team that's halfway across the country and isn't particularly good, just because they have players that went to the local university. The players know this, the networks know this, and they give the people what they want.2
1 Eight states do not have an FBS team: New Hampshire, Maine, Rhode Island, Montana, Delaware, the Dakotas, Alaska, and Vermont. The combined population of those states is less than 9 million out of the 322 million living in the fifty states.
2 I'm not even touching here on the secondary issue of "my school is better than yours because we put more players in the pros". This answer is plenty long enough already. That's also why I didn't mention Division 2 football or try to address cultural differences in the South vs. Northeast vs. West, etc.