People object to "cis" for at least two reasons:

First, it assumes that people are male or female because of their gender identity rather than their biological sex. For people who believe that biological sex is real and that acknowledging it is important for purposes of rights, safeguarding and clear communication, using "cis" is therefore a loaded term.

Second, while I'd say that many people who espouse gender identity ideology (by which I mean the belief that we are male or female because of gender identity rather than sex) don't wish to reify sex stereotypes, in practice that tends to be what gender identity boils down to. Eg a little boy will play with dolls or want to wear dresses; this is taken as proof he is "really" a girl. Stereotypes limit both men and women but they tend to be more harmful for women and girls. To call a woman "cis" is therefore taken to mean that she identifies with the stereotypes associated with her sex, stereotypes many women find degrading.

In your explanation of the term you say it just means "this side of" - can you expand on this? This side of what?