cellio | daf bit: Zevachim 64

The mishna teaches: all who ascended to the altar went up by the right side and came down by the left, except for three cases: a libation of either wine or water, or the burnt offering of a bird if other offerings are already burning. Why? When ascending one would walk most of the way around the altar before beginning and there are concerns about the smoke: the libation could become smoke-laden and the bird could die from the smoke before being slaughtered. So in these three cases the person making the offering takes the direct route. This reasoning is disputed in the case of the libation, with some saying he walked around the altar first and was then given the wine. (64a-b)

In the torah service today it is customary for the person receiving an aliyah to come up on the right and go down on the left, but for what appears to be an opposite reason: the altar service introduced a delay for the sake of ceremony, while when going up for the torah one is supposed to take a direct path.