Are these the relationships that you have?
Animals::Animalnumber = BreedingHistory|MaleAnimal
There are two ways to set up an "OR" relationship. One is to use a "join table" where you have one record for each value in your list of "or" matches:
Animals::AnimalNumber = ParentGender::animalNumber
BreedingHistory::__pkBreedingHistoryID = ParentGender::_fkBreedingHistoryID
A field in ParentGender would identify the animal as the male or female parent
but now you can access the related sets of records in BreedingHistory via the same relationship for both male and female animals.
But there's also another way:
If I have the above relationships correct. You can define a calculation field in breedingHistory, cParentIDList as:
List ( MaleAnimal ; FemaleAnimal )
And then a relationship of Animals::animalNumber = BreedingHistory|BothParents::cParentIDList
will match to Breeding history records for both genders. This exploits FileMaker's rather unique method of matching values when the values in the match field are a list of return separated values. In such cases, The record on the other side of the relationship will match if its match field matches to any one of the listed values in the match field of the other table.