Having watched Ant-Man and the Wasp I cannot see any decent reason why Ant-Man was not included.
In the beginning of Avengers: Infinity War, it's mentioned that Scott took a plea bargain, and this is played out in Ant-Man and the Wasp, 2 years house arrest and 5 years probation.
Without explaining the film entirely, stuff happens but towards the end of the film, he has this heart to heart with his daughter about helping people vs finishing his house arrest and staying clean. The outcome is that he suits up to save the day.
At the end, everyone is fine and there is a montage of people doing stuff, Scott having his tag removed, his friends doing stuff in their office, Scott takes Cassie out for the day. Hurrah happy ending!!
As the post credits scene reveals, this all happened pre-snap of doom. We see a scene where Scott is Ant-Man again, hanging out with the Pyms (which is a violation of his parole) and about to do some more Quantum Realm stuff. Then the Snap happens.
Given that we know there is a clear few days between the end of the action in the film and the finger Click of Doom, I feel there is no good reason for him not to be involved.
Here are 2 reasons I have heard and why I feel they don't stand up:
a) He is on probation and didn't want to be seen publicly. - In the film he has run this risk multiple times and even goes Goliath size to mess with a ferry in the water. I think he would accept the risk given the attacks in New York.
b) The Avengers don't call him and respect his plea deal. - I think the Avengers still watch T.V./The News and would have seen him as Ant-Man and so would've been aware that he happy being Ant-Man. They would have called to say "Hey, I see you still being Ant-Man, we need you if you want to come?" Even if they don't ring him, do you think he would have ignored the attacks in New York mess around on a roof top with a Van Sized Quantum Tunnel?
Has anyone read any other reasons why Ant-Man wasn't in Avengers: Infinity War that still makes sense?