to explain it you need some Physics, which you may or may not have. I don’t kniw.
Go and research:
Work = force x distance
Power = force x speed
Power = energy / time
gravitational potential energy
Power required
Power available
Excess power
and you’ll see why rate of climb relates to power (specifically, excess power)
Climb angle is a bit easier:
research the definitions of the orientation of the forces on an aircraft
look to see how the forces relate to one another in a climb
you will see that the geometry of the forces is related to thrust (specifically, excess thrust)