Airlines set their MCT (Minimum Connecting Times) for their connections* at airports they serve. These times are shared with all other airlines, put into systems which cannot be overridden by the average agent.
The costs to airlines for misconnects of passengers and of baggage can be significant and it is a major inconvenience for the customers. If they don't think they can make the connection, experience has shown them it's much better to rebook the customer onto other flights.
*connections meaning:
connecting flights on same airline/same terminal;
connecting flights on same airline/different terminal(s)
connecting flights to/from select airlines/same terminal
connecting flights to/from select airlines/different terminal(s)
connecting flights to/from all other airlines/same terminal
connecting flights to/from all other airlines/different terminal(s)
In the old days when the MCTs were published in the monthly airline guides some airports information were published over multiple (four column) pages.
It can be irritating when a small change in time affects a connection and you will find that (most) airlines will not insist you take it or leave it. If you call them you should be given other routing options or a full refund.
Other airlines are not so flexible, for example this is a message I got from U2 recently (translated from French):
If these hours do not suit you, you have the opportunity to rebook on our website
Réservez des vols pas chers vers toute Europe | easyJet in "Manage my bookings".
EasyJet standard conditions will apply in the context of this change, the General Conditions which can be viewed on our website.
I take this to mean they will not waive their rebooking fee - which is not on when they are changing a key contract term without my agreement.