The general rule in this case is that a PC cannot cast spells as rituals for classes which do not have the ritual casting class feature.
The Oath of the Ancients Paladin does not have ritual casting, and thus could not cast speak with animals as a ritual.
If the paladin multiclassed into wizard, he could cast speak with animals using his wizard spell slots per the multiclass casting rules, but he could still not cast it as a ritual because it is not in his spellbook (and likely won't ever be, since it's not a wizard spell).
If the paladin instead multiclassed into druid, he could cast speak with animals as a ritual following the normal process for druid ritual casting. Speak with animals is on the druid spell list as a level 1 spell and is tagged as a ritual spell.
Unlike spell slots, multiclass characters do not share prepared spells across classes. In order to cast speak with animals as a ritual you would need to have it prepared in your druid prepared spells. You could not cast it as a ritual from your paladin prepared spells.
This means that even though the Oath of the Ancients always has speak with animals prepared, he cannot ever cast it as a ritual without preparing it separately with a class that has the ritual casting feature.
On the other hand, even though it is limited to a number of uses per day by the character's spell slots, the Oath of the Ancients paladin always has speak with animals prepared and it does not count against his prepared spells.