From my perspective, there are four general categories people tend to fall into:
2. "Uninitiated gamers" These are the people who have an appetite for strategy and who gravitate to gamer's games right off the bat when introduced to them. They are simply gamers who have not yet encountered euro-games. (I was an "uninitiated gamer" who tried to make the best I could out of the games I knew about until I encountered euros and realized what I was missing.) You can introduce games like Puerto Rico, Tigris and Euphrates, and The Princes of Florence to people in this category with no problems.
3. "Potential gamers" These are the people who, given enough of the right kinds of early positive experiences with gaming can warm up to the heavier sorts of games over time to greater or lesser extents. In many cases, it's probably important that these people not be hit over the head with early gamer's games lest they potentially become resistent to the idea of learning future games. It's also probably true that each person in this category (as opposed to "uninitiated gamers") has a personal "weight limit" in that there is a certain level of complexity that they are unwilling to go beyond with their game choices. If a game exceeds that weight limit then they consider it too complex and pass on it.
4. "Non-gamers" These are people who, for the rest of their lives, will probably be averse to heavy strategy games - regardless of what games they are exposed to and in what order. There's nothing "wrong" per se with non-gamers. It's just useless to try to get them to like heavier games because what non-gamers look for in a game is typically social interaction without the "bother" of heavy strategy.
Something that most gamers experience is the frustration of trying to play the games that they enjoy with their non-gamer friends and, unfortunately, a bad experience is what they get. After enough of these types of bad experiences, it can be easy to just "give up" on playing games at all with certain friends.
Concerning this subject, I've tried adopting the philosophy that it is better to accept what is than to try and make something what I want it to be even when it's not. In other words, I don't try to turn non-gamers into gamers. I will, however, give someone the benefit of the doubt if they express a genuine interest in learning a gamer's game (if someone I consider to be a non-gamer really wants to learn Puerto Rico then I'll teach it to them).
I also believe that some people simply haven't realized that they might actually like some of the harder games. They just need to build up to them with enough positive experiences beforehand. Throwing a non-gamer directly into a gamer's game without positive prior gaming experiences will leave them in a position where they will be less inclined to like the game and more inclined to resist the game. However, helping someone "work up" to the heavier games requires knowledge of enough different titles that will appeal to gamer and non-gamer alike such that you have a variety to choose from along the way. Otherwise, if there are only one or two games you're aware of that you know you and your non-gamer friend can enjoy, then those games might not be enough to provide the variety and quantity of positive experiences necessary for a non-gamer to be open to learning heavier games. At that point, not only will upward progression towards harder games stop, you will also probably get stuck playing those same few games over and over again such that you and your friend(s) will get sick of them and eventually won't want to play them anymore.
I also believe that "needing" someone else to like something or trying to "get" them to like it potentially sets one up for disappointment because such a mentality does not leave one emotionally free enough to accept an unsuccessful gaming attempt as okay. I'm willing to try giving a non-gamer the opportunity of liking a gamer's game but I'm also willing to be okay with whatever results. In other words, if my non-gamer friend is hating the game I'm trying to show them, then I'm not above proposing that we just quit and do something else (perhaps even having a mutual laugh in the process about just how lousy the idea of playing that particular game was in that situation).
I believe, for a person to have enough emotional freedom to be okay with such an unsuccessful outcome, they need to have two things:
1. Knowlege that, if they were they one who brought up the idea of playing the game in the first place, they gave the non-gamer enough positive gaming experiences beforehand such that that person's dislike of the game was due more to that person's personality rather than because of a lack of experience.
2. A reliable venue for playing gamer's games (like a local game store, or BSW) that is not dependent on the non-gamer friend or friends in question. Without such a venue, if one wants to play heavier games, then one is going to have to "get" one's non-gamer friends to play them. This can lead to one of those afore mentioned "bad experiences" because, even if the gamer succeeds in coercing his or her friends into a game they don't want to play, it's still a game they don't want to play - thus creating some potential resentment and/or more resistence to the idea of playing that same game or same type of game in the future.