How would antifreeze get into my oil?

You probably have a breached head gasket. This will lead to antifreeze in the oil and can lead to a no start due to lack of compression.

The repair is to replace the head gasket. However, if you have been running around with antifreeze in the oil for a long time then you’d be better off either getting rid of the car or getting a whole different engine or complete rebuild of this one. The water/antifreeze mix in the oil will make a terrible mess of the engine’s bearings.

Didn’t your mechanic tell you this?