The reason that you can’t import into this field from the Contacts table is because this is a linked field. The field itself comes from the Entity table.
If you plan on using this field, you should know that because the relationship from Entity to Contacts is one to many, all contacts linked to the same entity would have the same value for the BirthDate field. If this is what you’re looking for, then this should work, however you will need to import the BirthDate into the Entity table instead.
Based on the fact that you are trying to import this value into the Contacts table, I believe you may want to give each individual contact a birth date. In this case, you will need to create your own custom DateTime field on the Contacts table to use for storing the birth date.
I hope this helps.