A CARPENTER literally means「one who seizes, grabs ahold of」and in the case of this ARTISAN, SKILLED WORKER, one who grabs or seizes hold of some sort of wood. Ancient form of this glyph was drawn with「short hairs, fur pelt, many strokes」(㣉) added and referred to「the delicate zone, skill required, the place where labor occurs」with 'labor' being physical or mental exertion, especially when difficult or exhausting work. The process by which the birth of a mammal occurs, beginning with contractions of the uterus and ending with the delivery of the fetus or infant and the placenta.
[ https://www.thefreedictionary.com/labor ]
Perhaps skin with fur seams were stitched together as the first garments.
Often drawn in Japan as the elements「upper rod」and「lower rod」pinched together with the vertical stems making contact, depicts a CLOSED SEAM OF FLESH, a CLOSED ORIFICE, two opposite sides of flesh around a wound or some natural orifice, or two animal skins that are being pinched together forming a seam…more permanently joining the two sides of that seam by suturing it closed requires SKILL, CRAFT, and certainly some kind of PLANNING.
Regaining immediate access to an orifice that is being held closed or pinched temporarily also requires SKILL, CRAFT, and certainly some kind of PLANNING. Also meaning an ANUS or some other FLESH SEAM but still with some deliberate pinching tension holding the sides closed of the rectal sphincter, perhaps due to a deeply-seated fear and trepidation of what is to come, or, due to the knowledge of an experienced service provider.
An as yet CLOSED ORIFICE while still in the bargaining stage of early human bartering that TRADED sex for food, with one person having SPECIAL SKILLS, a PROFESSIONAL who could PLAN and produce results much better than others, and could specialize in hunting for others less skilled, or those folks having sexually-related abilities to TRADE with others, hence the English word also refers to TRADING what one can do (having a TRADE, the first professions of males hunting and females prostituting) in exchange for what someone else has or can do.
With「hand」element (左), depicts someone stitching two animal skins, or a large flesh wound together by holding the left side closed in preparation for the needle and thread, while the right side remains open. Consider that other than sex, the very first labors of early humans were necessarily all individually provided services, such as weapon-making and hunting meat for that evening's supper. The next job was likely the CRAFT and LABOR of producing clothing from the animal hides as skin protection. While a simple hairy hide could be draped over a cave person's shoulder as in a Hollywood movie, it is far more likely that some SKILL was applied to create clothing that was less drafty and more functional, clothing manufactured by one person having SPECIAL SKILLS, a PROFESSIONAL who could PLAN and produce results much better than others, and could specialize in making clothing for others less skilled, having something to TRADE with others, hence the English word also refers to TRADING what one can do (having a TRADE) in exchange for what someone else has or can do. Naturally, after textiles were manufactured on a loom thousands of years later, this same CRAFT, SKILLED LABOR meaning still applied.

External source definitions …excluding politically incorrect concepts and other meanings deemed offensive today; may include extended definitions, euphemisms, and mnemonics)
Chinese: work; worker; skill; profession; trade; craft; labor
Japanese EDRDG: craft, construction
Unihan extended: labor, work; worker, laborer

Used within names (nanori)
もく