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.
What is love?
I am now 46 years old, and I have no idea what "love" is or what it means when I myself say that I "love" someone.
To my knowledge, "love" is not a concept in psychology, but in philosophy, where speculations about transcendental ideas such as "freedom", "truth", or "evil", are at home, or in sociology, where the norms relating to these ideals are studied.
Related psychological concepts are:
Psychology studies what people do and how they feel, when they call it "love".
But let's ignore these objections for a minute and assume that we know and agree upon what love is. Let's take an everyday definition.
If you understand love as selfless commitment to another's wellbeing, then young children are not able to love (because their only purpose in life is survival, not generativity), and able to understand love only from the perspective of the rightful receiver: they are "made" to expect parental love and cannot comprehend that it might be modulated, because their survival and development depends on its presence.
Children learn to understand that other people might have different things going on in their minds than they themselves, and they learn to consider the needs and wishes of other persons, from about the age of 6 years onwards, a development that (ideally) reaches its conclusion (i.e. full understanding) at about the age of 12 (with all the individual variation that is normal for human beings).
Therefore a young child will not understand a parent's statement that they love all their children equally from the definition given above (or any other such definition), but interpret it from the context: what did the child, its siblings, and the parents do, that led up to make such a statement necessary in the first place? Just take a minute and think about if and when you would say such a thing to two persons you love. Only when there was doubt that you loved them equally.
Thus, the meaning the child gives to this sentence might be: We treat you differently, but we expect you to act as if we didn't.
So a child will very likely not think about anything like what adult philosophers understand when they speak of love, but about how his or her family interacts with each other and how he or she feels about that.
If you disagree with my statement that love is not a concept in psychology, please provide a source and quote a peer reviewed definition.