"Aamir loves his family."
Translation:आमिर अपने परिवार से प्यार करता है।
Think of the sentence as being similar to "Amar is in love with his family". The से functions similarly to the 'with' in this sentence.
'प्यार करना' can be used with the postpositions से or को (with से being far more common). The meaning is pretty much the same in both cases but with a very subtle difference. With से, you are in love 'with' someone and with को your love is directed 'at' someone.
Would आमिर उसके परिवार से प्यार करता है also be an alternative? At least it is rejected...
That can also translate to "Aamir loves his family' but when the 'his' in the sentence is not referring to Aamir.
For example, consider these two sentences:
आमिर पीटर से प्यार करता है। वह अपने परिवार से भी प्यार करता है। - Aamir loves Peter. He also loves his (own) family.
आमिर पीटर से प्यार करता है। वह उसके परिवार से भी प्यार करता है। - Aamir loves Peter. He also loves Peter's family.