No it is not normal! If you can't paddle it effectively you can't catch waves , can't make turns or snaps or any other thing.
The waves you catch on a poor paddling board will be late drops or over the fall take offs and you will not have the wave speed to make much of a wave.
The turns you need to learn are a flow from one fully committed turn to another turns gaining speed in each turn.
A starting sequence of turns, initial bottom turn swung into an effective top turn / and degree of cut back turn. Another bottom turn or even the first one if it is well done and powerful will allow you to put much more direction change power and control into the top turn. Do that well enough and sudden enough and a snap is born.
Where or how did you learn that short boards do it easier. ( sales person?)
BTW don't buy the sales pitch that only short boards can do this, it take s the skills of the rider to do it ,
even on longboards
Really get your moves rocking on your longboard and then come down you are light enough to do that! Consider too a short board with more volume , up the floater quota and catch more waves. Get more wave time and hey presto your skills will improve
