For the question, "I love going out with you," wouldn't one use the familiar you "me gustas" instead of the (subject: usted/she/he/it) "me gusta?"
In "Me encanta salir contigo" we're not using a subject usted, él, ella...
With encantar (same as with gustar) the subject is actually "what one likes", in this case, taking the form of an infinitive in Spanish: "salir contigo".
If you read this lesson about gustar you will see why we use me gusta here. Have a look.
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