A household task becomes unequal when remembering it belongs permanently to one person.

Splitting a chore in half does not split the work of keeping it in mind. One person notices the empty shelf, tracks when the bin goes out, remembers that the appointment needs booking, and that noticing runs all day whether or not anything is being done. Help offered on request still leaves the requesting to the same person, and requesting is most of the burden.

Try handing over a whole task rather than a turn at it, including the deciding when. If you are the one carrying most of the remembering, name one specific thing and pass it on entirely rather than asking for more help in general.