CD rates are still low, but interest rates are rising. Why is that?

Banks, to stay competitive, make adjustments on interest, be it rates or yields.

Depending on where they want to compete on a market level, they may lower their mortgage rates but keep their cd yields low, or vice-versa.

I would prescribe you shop for CD's. A lot of major banks have competitive mortgage and autoloan rates but their cd's tend to be low yielding.

Some credit unions, smaller banks and even some insurance companies have far better cd rates. I believe State Farm cd rates go up to 3%!

Because interest rates on 30 year mortgages have been low for years, and will stay low on the mortgages issued. Banks need the spread to make a profit.