You can show your parents the Aswattha Vriksha Stotram. According to which the tree itself is the abode of the Trinities (Brahma, Vishnu and Maheswara).
Moolatho Brahma roopaya, madhyatho Vishnu roopine,
roopaya Vruksha rajaya they nama., 1
My salutations to the king of trees. Whose root is the form of Brahma,
Middle is the form of Lord Vishnu, And top is the form of Lord Shiva.
The other points that you can say in it's favor are that, if adored/taken care of, it is the bestower of riches, longevity, progeny etc, which all human beings love to possess.
Also, the presences of the deities in the tree will by itself take care of the fact that evil spirits don't wander nearby. So, your parent's apprehension is unfounded here.
See the various verses from the same Stotra given below:
Ayurbalam yaso varcha, praja pasu vasooni cha,
Brahma prajnam cha
medham cha thwam nodehi Vanaspathe., 3
Would you not give me, Oh product of the forest. Long life, fame,
splendour, children, cattle and riches, As also knowledge of God and
Akshi spandham bhujaspandham duswapnam dhurvichinthanam,
Sathroonam cha samuthanam hyaswastha samaya Prabho., 5
Oh Lord Aswatha, please control pain in the eye, Pain of hands, bad
dreams, bad and evil thoughts, And help me in destruction of my
Aswathaya varenyaya sarva aiswarya pradhayine,
nasaya, suswapna phala dhayine., 6
Oh Aswatha who blesses us and grants all type of wealth, My
salutations to you, who destroys bad dreams and grants good dreams.
So, there are some good points you can recommend about the tree to your parents.
But having such a big tree in the compound of the house can be problematic as well and the garden should be quite big to accommodate it. The tree is extremely dominating so it will take control of the whole garden and it is likely to create wreckage in the surrounding walls too.