I may be the only person in the universe who does this (or maybe it’s an yet-to-be-discovered but harmless chronic condition?), but I have from childhood gendered everything. In an email entitled, “Your services are needed,” my husband alerted me to this controversy. I can say with certainty that the knife is male (and in my childhood heterosexist view, the father), the fork female (wife), and the spoon male (son) and salad fork female (daughter). Pepper is male and salt female.
This is the first I’ve come across the rhyme, and the best I can guess is that cultural notions of gender (size and proportion foremost in this case) are so endemic that a tall piece of silverware with mainly straight lines would appear male to me (and others, apparently), and a piece with a curvy ‘shelf’ that would remind one of breasts or hips would appear female. Beyond that I have no explanation beyond my own possible psychosis.
Do let me know if any controversies arise about the genders of various models, makes and colors of cars, towels, chairs, backpacks, spices, or refrigerators, as I will undoubtedly have an answer.
Everything is a bit unusual, but numbers, letters, days of the week, months of the year, colors, etc., are quite common, so don’t worry about it. Just be aware that not everyone does it, and that those who do often disagree. Similar phenomena involve perceiving abstract things as colored, or fitting into odd-shaped lines (see Number Form in Wikipedia).
I don’t really know Baltic either, but the similarity comes because Lithuanian, Latin, and English are all Indo-European languages. Lith. menuo is presumably related to English moon and month and to Latin mensis (“month”), all of which come from the proto-Indo-European root *me- (to measure). The usual Latin word for the moon, luna, is from a different root, related to English light and Latin lux. English sun, Latin sol and Lithuanian saule are all from the PIE root *saw-el- (“sun”).
The asterisks indicate the forms are reconstructed and not attested, because PIE was not a written language.