Eggs turn into chickens at a different rate than chicken turns into eggs. This is proof either that A) time must go forwards, or B) my proof has a logic flaw in it.
....or C) that you forgot to account for entropy. To study time reversal violation you must have two states with identical entropy or you must account for the effects of entropy. The reason that a glass falling from a table and shatters is far more likely than all the pieces of glass coming together, leaping off the floor and forming a new glass is because of entropy. There are countless ways in which a glass on a table can be converted to broken shards on the floor but starting with the shards there is only one way that that process can be reversed.
Scale the system up, and they're just little birds that fly in boring ways, don't time travel, don't fly faster than light,...
Ummm...yes but the reason for that is because the fundamental physics governing the particles of which the starlings are made up prevent time travel and moving faster than light (which are actually one and the same). Assuming you are building a model out of simple, plastic lego bricks then regardless of what you are building we know that it will not be a conductor of electricity because the bricks you are building it from are all plastic insulators. Studying the fundamental physics of a system lets you know what is possible.
For example we know that there is a fundamental arrow of time despite the fact that at an everyday scale this is completely obscured by entropy. You could study all the flocks of starlings you like but it would be impossible to show that you have time reversal violations in it...and yet since the particles in that system are subject to the weak force we know that at some incredibly tiny, insignificant level it is there.