AA's on-time fixation is crazy. This weekend, was flying MIA-DTW at 13:36. At about 12:45, I received a text that departure was now 14:00. I made my way to the gate -- arriving about 13:20. At that point, they announce that the delay is because there are no pilots available and that they will arrive in Miami at 14:00. At 13:30, they begin boarding the plane "so that they will be ready to go when the pilots arrive". I realize that there will be no way that we will depart before 14:30 and decide to sit in the gate area, rather than board. (My seat was in F on an A319). Almost immediately after they call Group 9 and the last passengers board, they page me to the counter. "Are you planning on getting on this flight?" Yes, I answered. Well, you need to board now or we will give away your seat, I was told. (All through this time, the AA app and the monitor are still showing a 14:00 departure.) I boarded the plane and of course, we did not depart until 14:45. So, when is T-15 or T-10 when AA shows departure at 14:00 even though that is completely impossible?