You gave that book to your mother? Interesting. My understanding is that the Buddhists don't avoid love, rather they try to develop an unselfish love that is beyond the capacity of most people. So it is not so much that they avoid love, it depends on what your definition of love is. Buddhists develop a great deal of lovingkindness for themselves and if we look at Christianity, Jesus is recorded to have said "love your neighbour as yourself." So the question also becomes how do we love ourselves? Buddhists give a lot of methods on how to love oneself, so they can love others, love their neighbours.
I don't think Buddhists are doing something strange since Jesus also teaches to love the neighbour as thyself. Again it depends on your definition of love. Buddhists try to develop a more non-selfish love, lovingkindness that enables us not to be hurt so much when others don't love us in return. I think this Christian writer may not understand the Buddha's teachings, as I understand them and the Buddha.