Coming out of the water, he ran furiously up against a hill, and with the same alacrity and swiftness ran down again. He climbed up at trees like a cat, and leaped from the one to the other like a squirrel. He did pull down the great boughs and branches like another Milo; then with two sharp well-steeled daggers and two tried bodkins would he run up by the wall to the very top of a house like a rat; then suddenly came down from the top to the bottom, with such an even composition of members that by the fall he would catch no harm.
Usually, when humans (or humanoids) are compared to animals in literature, it is to denote a wild, uncivilized trait. This is used interestingly in almost the opposite way here: Gargantua is compared to a cat in agility and light-footedness, a squirrel in climbing and acrobatic ability, and even a rat in wall-scaling. These are all positive, even elegant connotations. Although Gargantua is being compared to animals, it's not to point out savage or uncivilized habits, and as we see him become more educated and accustomed to the 'proper mannered' way of life, we see a shift into the more precise, controlled movement that is highlighted here.
https://wordsliketrees.wordpress.com/2019/10/20/personification-zoomorphism/