From the introduction of nether portals in Alpha v1.2.0 up to snapshot 12w17a inclusive, when entering a nether portal, exiting from the other side would start the player with the nether portal animation at full intensity, but with it rapidly drawing to a stop due to the player not being able to teleport using the portal.

With the 12w18a singleplayer client-server logic split, among other broken features, this slowdown effect no longer occurred, and the player would be placed in the other dimension with no effect active at all, which is mildly disorienting.

As of 12w34a, MC-180 came into effect, making this bug considerably harder to see. It can still be noticed by the nether portal effect not beginning at full intensity, but rather increasing like it would upon first entry.

Fixing this alongside MC-180 is recommended. A table showing the changes in behaviour and what is desired can be found as follows: https://minecraft.fandom.com/wiki/Java_Edition_12w18a/List_of_broken_features#Nether_portal_exit_animation