Air Canada won’t take responsibility for their mistake

My partner and I were flying from Colombia to Vancouver with a layover in Mexico City. We had a 3 hour layover so decided to hang out in the lounge. Originally departure time from Mexico City was 05:50. At 04:42 am, shortly before we were going to head to the gate, we get an email that I’ve included below. It says that the flight has been delayed until 06:45 due to air traffic control restrictions. We decided to hang out at the lounge for another hour and show up to the gate at 05:45, an hour before the flight was going to take off. When we get to the gate, the desk agent tells us they don’t know how this email was sent but it was an error and the flight boarded on time and the gate is now closed and we can’t get on. Air Canada is unwilling to help and provide compensation and instead kept saying “you were late for your flight” despite them sending the email. I suspect their system messed up with the time change but that’s not our fault. We then try to get our bags back and they are very unhelpful. Eventually one desk agent says “go to carousel 20, you can find it there”. He said this without looking anything up, etc. We called him out on this and said it seems like he made this up just for us to leave and him and his coworkers started laughing. Customer service over the phone as well have been unhelpful and kept reiterating we missed our flight because we were late. They can’t comprehend that we were “late” because they emailed us telling us to be late.