Like Ulanopo said, the biggest reason Riot had to withhold precise feedback on Honor Progress is that it would gamify the system and tell people "you have this much left to do before you get your next reward!" - it shouldn't be an arbitrary math problem of "how many Honors do I need to get/how much progress can I get to get to Honor 5" - the incentive of the Honor System is that you're supposed to want to be positive, sportsmanlike, and Honorable.
They want Honor to be a slow, gradual thing, sitting on the sidelines - not a main-focus grind. They want you to be aware of your Honor progression throughout the year, but not directly trying to push a little meter higher and higher.
On top of that, if they gave people a meter for Honor progression, they'd have the math behind Honor progression figured out in no time flat. And, again, that leads to no mystery, no excitement, just "oh, hey, I'm x amount of games with team honors away from my next milestone. woohoo."