Here are a few reasons:
The long half-life of T4 makes it take 6-8 weeks t reach a stable level in your blood.
Having too much med or being hyper for other reasons increases the level of thyroid binding globulin in your blood. This protein hangs on to the T4 to keep you from going as hyperby keeping you free T4 down some. When you start reducing your dose, the body sees less need for the thyroid binding globulin and releases some of the bound T4 in the process, so your Free T4 level doesn't drop as quickly as you would initially think.
If you have bee hyper (or overtreated) for an extended period, the tissues are over-saturated with thyroid hormone and it takes longer to correct this than it does to adjustlevels in your blood.
The opposite is true for hypothyroidism (or being under treated). The tissues are starved and it takes more time to get the the hormone they need and let the healing start than it does to get the levels right in your blood.
I am not a doctor, nor have I ever played one on TV...