Is the concept of conservation fundamental to understanding fairness and capacity in "love"? I heard this comment on a radio program about Child parenting by psychologists: "A child will not comprehend an explanation that, a parent loves each sibling equally, as they do not have abstract thinking". This lead me to ponder and formulate the question.
There are a number of ways to interpret the statement and your question. 

One problem is what the age of children being discussed is. There are lots of developmental studies showing abstract thinking not really kicking in until about 5 or 6, but most of them are on physical abstraction. You can look up anything on Piaget's stages of development for this. Abstraction in general id acquired relatively early.

The word "understand" is a problematic bit. Children understand fairness, equal division, etc. at a very young age. I don't even see that as particularly abstract. On the other hand, some people spend their whole lives trying to understand the nuances of what love means. Children have some concept of love at a pretty young.

As near as I can tell, the statement you heard is vacuous without context and intent.