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The Day Care Man can often be very misleading. If he describes your Pokemon as not liking each other, that actually means that they will breed, but their chance of producing an Egg with each egg cycle is low. This requires further explanation if you’re unfamiliar with the internal mechanics of breeding.
The chance assigned to your Pokemon per egg cycle is based on their species and whether or not their original trainers are different from each other. If you pair two compatible Pokemon with the same species and a different original trainer in the day care, their chance per egg cycle will be 70%, and the day care man will say something like: “the two seem to get along very well.”
In order for you to get an egg you have to have the final evolution breed with a ditto or with other Pokemon in the same category of the Pokemon you want in the egg. For example: You would need to breed ditto with an Alakazam.