The 'default' function you are referring to, is for iPhones dual SIM iPhones with both SIM card active. It allows you to choose which line (SIMCard) should be used as default to call or text person. This option has nothing to do with how many phone numbers you have saved under one contact card.
In other words, if you have two or more phone numbers saved under one contact card, to call the contact tap on the number you wish to call it.
If you want to text the person, when you tap the quick action 'Message' button appearing underneath contact name, that will bring you to the thread in Messages app you have started already when messaging with that contact. If you want to message the person to their other number, do a long tap (or tap and hold as some calls it), then then choose the number from the menu you wish to send the message to. Otherwise, in Messages app, tap new message and in "To" field type in the phone number you wish to send the message to.
In Phone app, you have Favourites tab, where you can add 'favourite' actions so when you go to the Favourites tab with single tap on the entry you can call the contact on selected phone number or to message the person on selected number (tap on that option will bring you to the Messages app).