You can isolate cells very easily from your own person or from volunteers, usually without too much pain. And, for example, I've done it to myself and I'll illustrate it. You can pinch, for example, part of your tissue like your wrist until it's a bit numb. Then you pull up one hair with a forceps, so you have a pyramid of skin, then you knock the top of that pyramid off with a sterile scalpel, with a bit of pain obviously, but easily endured, and you take that hair with its attached skin, put it into a vessel that contains an enzyme called trypsin. The trypsin dissolves the substances that keep cells together in a tissue. Very much like a brick wall and what you're doing is dissolving the mortar in a brick wall and releasing the millions of cells, and there are millions of cells, in that tiny scrap of tissue, and now you take those cells, put them in a growth media.
The media consists of chemicals that are well known, that you might expect, like amino acids, certain salts, sodium, potassium, calcium, phosphorous, etc. And because we do not know, for most cells, certainly normal cells, what their growth requirements are in chemical terms, we have to cover our ignorance by including in the media serum from an animal. Usually about 10% of the volume of the growth media consists of serum. It might be humbling to realise that your own cells, or human cells, grow very well in serum from a cow, a horse, or several other species. You do not need human serum to grow human cells, although they will grow in human cells, but that obviously is much more difficult to obtain, more costly. So generally people use bovine serum as the cover-up for ignorance and that continues to this day.