I have a 28 year old house. The linoleum need to be replaced in the
bathrooms and the front door landing. I intend to use 13" x 13"
ceramic tiles. A neighbor who had already done his recommends that I
add a plywwod subfloor so that the base will be rigid. This is to
prevent the tile cracking. I would prefer to glue the tiles directly
to the existing floor. 1. to keep the floor thickness low, 2. skip a
lot of extra work, 3. In 28 years the floor seems very stable and
does not creak or "bounce."

Is a subfloor absolutely necessary? If so how does one fasten this
subfloor to the existing floor - glue, nail or screws?