I used to work for a major American airline and flight schedules usually change around the fall and spring seasons to accomodate the increase in air traffic for the summer and winter season (ski and south destitation spots). However, when changes are made, they rarely move individuals off of flights. The only reasoning behind this would be that the originial flight that was booked is no longer available, meaning they cancelled that segment of the flight pattern. Most airline have the flight time changes of their schedule already built into the reservation system when you intitally book the flight so changing to another flight should not occur. I would contact the airline directly and ask for an explanation. If the CSR on the phone can't give you an adequate answer that you are looking for, ask to speak to someone above them. There is always a supervisor at each of the call centers and at the airport location that can assist you. If they moved you off of the flight for no apparrent reason, demand to be back on the originial flight. If that fails, DOT laws require compensation for being involuntary being denied boarding (or in this case, being involuntary moved to another flight without your consent)on a commerical flight in which you have a paid ticket for.
As far as slot at the airport...The previous post hit in directly on the spot. The individual airport authority and DOT get together each month with the sales and marketing departments of each airline and work out their slots amongst each other. If say Delta needs a 6am departure to ATL and their are only 4 slots available due to traffic departures across the US at this time, Delta will then go to the 4 other airlines and try to work out a trade. I have seen them give up afternoon slots to other carriers in order to get that one departure in. (Meaning that they trade 2 takeoff and landing slots to another carrier for one departure and landing).
The gates are leased by each airline. I paid around 14000.00 a month just for the jetway. Once the jetway is leased, some airlines at smaller airports will work with each other in the event that a gate is needed and they have no flights on the ground or in their immediate flight pattern. In bigger airports, you will not see a Jet Blue aircraft at the gate of American unless they have they contract to handle that ramp and counter ops for that carrier. the old saying, to each it's own applies here.
Hope this helps clarify any questions.
Preston