Because you are mixing the rainwater with tap water you are diluting the minerals in tap water not removing them. The minerals in the tap water are still there, just not as many of them.
The minerals in tap water depends on what rock or soil the water has been in contact with since it fell as rain. If it dissolved minerals that cause high pH, they are still there when you mix it with rainwater which (in theory) is pure water with no minerals at all. So the mix still contains minerals which cause high pH.
If you were to use all rainwater, that would have no minerals at all in it so in theory the pH should be 7.0. I say 'in theory' because rain does dissolve things from the atmosphere as it falls which can alter pH slightly. This is the main reason why rain water shouldn't be used where there is air borne industrial pollution or agricultural pollution (eg crop spraying) and you don't want contaminants like that in a fish tank.
It is possible to use only some form of pure water (rain, RO etc) in a fish tank - we have members who do just that - but most people add minerals to the pure water which again, depending on the nature of the minerals, does change the pH.