In our Gemara on Amud Beis, there's an intriguing phrase used to describe young children's attachment to their mother: כרוכים אחריה, which I would translate as "wrapped up with her and following behind her." Rashi here employs a word that literally translates as attached, נדבקין.
The Gemara in Shabbos (141b) uses a different idiom to describe paternal attachment: געגועים, which translates as "pinings or longings" and is likely an onomatopoeia for a kind of wail, repeated over and over, as "ga-a, ga-a." (Two interesting points: In Hebrew, when a root is repeated, it signifies something that happens cyclically or repeatedly. For example, מפעפע for bubbling, אדםדם for very red, or גלגל for a rolling wheel. Secondly, Hebrew abounds in onomatopoeia because it's an original language. For instance, זבוב for a fly, which makes a buzzing zvuv noise. Or, to combine both repetition and onomatopoeia, we have the word for flask, בקבוק, because when you pour, it repeatedly makes a "bak-buk" noise, or in English, we might say, "glug, glug").
Reflecting on the different words used for maternal versus paternal attachment corresponds with the psychological differences between maternal and paternal attachment. In the case of the mother, young children are literally attached, wrapped around her, and following her everywhere. However, in the case of the father, the child is detached and pining to once again find and be attached to his father. In other words, the child ventured into the world and is now seeking to reunite with his father. The situation described in the Gemara Shabbos regarding paternal attachment involved a young boy holding a muktzeh object on Shabbos. In certain circumstances, it is permitted for the father to pick up the boy, even though he is holding a muktzeh object, because otherwise, the child would grow ill from the געגועים, the pining for his father. (See Rashi in Gemara Shabbos ibid.) Notably, the son is out and about in the world and discovers an object that puts his sense of personal agency in conflict with his father's agency. He wants to hold onto the rock but also wants his father to pick him up; the father faces a dilemma because it is forbidden for him to hold the rock. In at least some circumstances, the son's conflict must be respected, and thus the father is allowed to pick up the boy.
From a psychological perspective, attachment to the mother is based on emotional support. When the child receives empathy and emotional regulation from the mother, the child begins to internalize and develop self-soothing and regulation. In turn, attachment to the father supports taking risks, exploring the world, and being more adventurous (Bretherton I. Fathers in attachment theory and research: A review. Early Child Dev. Care. 2010). Think of a typical mother's behavior with a baby, cooing and reflecting each emotion and expression the baby has. On the other hand, the father throws the baby up in the air, and the baby is scared but also thrilled to take the risk and fall back into his father's arms. This process symbolically repeats itself throughout childhood in similar age-appropriate behaviors for both fathers and mothers, along gender lines.
Pure biblical Hebrew is fascinating because since the words originate from internal roots, each word tells a story. Here we see how the child psychologically attaches to the mother differently than to the father, and how these nuances are reflected in the Hebrew language.