I noticed that the Sumerian words for mother and father, ama and abba respectively, are very similar to the Hebrew words for mother and father, being ema and abba respectively. Given that Sumerian is not in the Afro-Asiatic language family, let alone the Semitic one, are the words for father and mother unrelated in each language, or are they Semitic loanwords into Sumerian (or vice versa)?
First off, it's worth noting that the main contact between Semitic and Sumerian involved Akkadian, not Hebrew, and the Akkadian words are a bit different—"mother" is ummu, and "father" is abu. And there was another Sumerian word for "father", ad(a); ab(a) probably originally meant "elder" (it's sometimes translated into Akkadian as šību, "elder" or "witness"). This makes the loan hypothesis a bit less likely.
But even so, this is a very striking coincidence. Compare also Navajo amá, Mandarin māma, Swahili mama, English mama, all meaning "mother". Why do all these words look so similar across the world? Surely they can't all be loanwords or cognates?
The main hypothesis is that it comes from baby-talk, the first sounds infants are able to make as they learn to speak.
/m/ is generally the first consonant they figure out, and
/a/ is the first vowel, so it makes sense that babies' first words would be along the lines of
/mama/. The same goes for words like
/dada/, which use sounds that get figured out fairly soon after. So the vast majority of the world's languages have words for "mother" and "father" that follow this pattern.
(It's also worth noting that many languages use the nasal sound for "mother" and the oral sound for "father", but this isn't a universal—you can also find many languages which have them reversed! The most famous example I can think of is Georgian mama "father" vs deda "mother".)