To elaborate on what LadyCFII said, you can only breed twin-fins from two other twin-fins. You can only breed spotanus from two other spotanus. All other fin varieties and body styles can be bred from other fish.

There is a very nice breeding chart in the guide section that you can use to see exactly what breeding any two fish will give you. there is a version for real excel and another version for the free excel viewer.

the one for the free excel viewer is probably better for learning how to breed your fish. the one for the real excel does all the work for you, but it is not as intuitive as to why breeding certain fish result in other fish. if you have the real excel, download them both.

if you look at the fin chart and also the body chart of the free excel version of the spreadsheet, you will notice that twin fin and spotanus are on the edge of the chart and in the body of the chart there is only one entry for twin-fin (where the twin-fin row on the left and twin-fin column on the top intersect on the fin tab chart) and there is only one entry for spotanus (where the spotanus row on the left and the spotanus column on the top intersect on the body tab chart)

if you can't find these in the guide section or have more questions, post them here, i (or someone) will do my (our) best to answer them.