I see the same thing in road cycling. The friend or spouse (whose an avid cyclist, the kind who lives in spandex when not at work and uses words like rpm, metric century and derailers), talks girl/boy/wife/husband into coming along on a ride.
Mostly I see a lot of apprehension, followed by a bit of anger and annoyance. Yup. Our enthusiasm is our downfall.
In yoga, as in cycling, the more experienced partner tends to forget that the newbie needs to be eased into the new activity. Someone newer to cycling is NOT going to be able to maintain a steady speed of 14 mph for 10 miles. No way, no how. Someone new to yoga is not going to feel comfortable in an hour and a half Ashtanga class. In both scenario's, the likelyhood of the newbie coming back is almost zero.
1) Ratchet back. Take your friend/spouse to a class geared more for beginners. Yes, YOU can probably hammer out 10 sun salutations in 10 minutes and hold boat pose with the best of them. THEY can't. Start simple. This is a great opportunity to look at a class with a beginner's eyes and work on some of the basic foundations of your asana.
2) Introduce them to the instructor and let the instructor know that they are new to class. A good instructor will know to keep an eye on their guest and offer modifications as necessary.
3) Don't set your friend/spouse/partner's mat in the corner, and don't let them do it either. Middle of the room or towards the back. This way they have a full view of the instructor and will have other people to watch. Back corner guarantees 'rubber necking'. Not good.
3) Once class has begun, leave your friend/spouse/partner alone. Way too often I see our enthusiastic practitioner 'adjusting' the newbie, telling them what do do. Let them be. They already have so much being thrown at them that having you telling them what to do on top of it can be overwhelming. Instead, focus on your practice and let the instructor watch your friend/spouse/partner.
4) If you feel compelled to offer encouragement, keep it to a smile, a whispered, "you're doing great!", a thumbs up. See #3
5) Try not to pounce on them after class with the question, "Well? Did you like it?" Give them some time to absorb what they just did. Ask instead (over coffee or on the drive home), "Do you have any questions about what we did today?"
6) And this is the hard one: don't expect them to love it. Don't expect them to even like it. Yoga is such a personal thing and not for some. Just like you may not be attracted to weight lifting, so they too may not be attracted to the nuances of yoga. And that's okay.
(picture from yoga clip art images)