Each fish quest, there is a series of probability "rolls"
The roll for the first is for a fish type, and the count is based on the last # of fish in a quest for that type that you got (10, followed by 15, followed by 20). Dismissing a quest of that type will lower your fish number the next time that comes up by 5.
Next, the quest checks to see if you get a second quest line.
The check for a second quest line is supposed to be based on (# of different eligible quest fish you've completed at least ONE quest for)/(# of total quest fish you can catch at your level).
So, until you've completed at least one quest for several fish types, you're probably only get 1-line quests.
(if a second line is indicated, the two rolls are repeated, this time with the second to third line check looking for the number of fish types you've done at least 2 quests successfully for, and so on, until there's the maximum 6 lines).
If you have an active 10-fish quest for a fish type, until you turn it in, any other quests you get wanting the same fish type will also want 10 of that fish (for the most part - if you turn in a 10, and still have another 10 for that fish on you, the next new quest for it will want 15).
This used to roll over 10/15/20/10/15/20 etc. before publish 72 - not tested to see if it still does. Some changes did occur for higher-rank fisherman to get off that rollercoaster (it was originally supposed to go 10/15/20 and stay there, based on early dev posts), but I've not pulled sufficient quests yet to see if it's done it for me.