Some of this comes from the way the film was made -- Frank Nugent's shooting script was heavily modified by Ford during shooting, and many of the hidden motivations and dark hints in the film were semi-improvised. (The famous silent scene that comes the closest to indicating the love and possible involvement of Ethan and Martha, the one where Ward Bond drinks his coffee and pretends not to notice the sexual tension between them, is not in the script at all. And Ford added the scene where Ethan shoots out a dead Comanche's eyes; the script called for Ethan to take his scalp.) But most of it is undoubtedly intentional. Ford liked to point out that many of the critics missed the fact that Ethan was supposed to be in love with Martha. If you don't get that sexual element, the movie becomes more of a standard revenge Western, and that's the way most critics treated it at the time.
The fact that so much in the movie is only hinted at makes it easy to speculate about other things the movie might be trying to tell us; that's where the fascination comes from. Because The Searchers constantly wants us to read between the lines and see what's really happening underneath the surface, it's tempting to look for all kinds of clues to hidden motivations, even ones that Ford might not exactly have intended. The most common speculation is that Ethan was not only in love with Martha, but that he might be the real father of Debbie. If you believe that, it changes the way you read Ethan's quest. Others have speculated that Ethan's whole quest is driven by sexual frustration over having lost Martha to his brother. Another line of speculation is that Ethan might be the father of Martin (Jeffrey Hunter); we are told that Ethan "found" Martin, but Ethan seems defensive and wants to change the subject ("It just happened to be me"). Other speculation involves the question of who taught Ethan the Comanche language and how this ties into his racism; when Ethan indirectly (of course) taunts Scar for having learned English from Debbie, Scar turns the taunt back on Ethan's knowledge of Comanche, suggesting that there might be a Comanche woman in Ethan's past. And so on and so on. There's about a dozen unmade movies lurking in the ellipses and penumbras of this one movie.
One possible interpretation that never occurred to me before is one I just found on a message board somewhere. A poster was writing about the scene where Brad (Harry Carey Jr.) thinks he's spotted Lucy, the older of Ethan's two kidnapped nieces. A distraught Ethan reveals -- as usual, without actually saying everything directly -- that he found Lucy raped and killed earlier that day. Here's the scene as written in the script, which made it to filming more or less intact -- Wayne's performance is of course incredibly powerful in the scene:
ETHAN (voice flat): What you saw wasn't Lucy.
BRAD: It was, I tell you!
ETHAN: What you saw was a buck wearin' Lucy's dress...
(they stare at him)
I found Lucy back there in that canyon...I wrapped her in my blanket an' buried her with m'own hands...I thought it best to keep it from you -- long as I could.
He can't look at Brad or at Martin. Brad can't speak -- and then finally:
BRAD: Did they...? Was she...?
Ethan wheels on him in shouting fury.
ETHAN (blazing): What've I got to do -- draw you a picture?...Spell it out?...Don't ever ask me!...Long as you live don't ever ask me more!
It seems straightforward enough, but a poster -- perhaps picking up on the fact that Ethan never specifically says that the Comanches killed Lucy -- wondered whether Ethan could have killed Lucy after he found that she had been raped. Remember, the rest of the movie is about Ethan's quest to find and kill Debbie for having been "defiled" by the Comanches; who's to say he didn't do the same to Lucy? Ethan is also shown with a knife not long after coming back from finding Lucy, though I can't remember exactly what he's doing with it.
Obviously, it makes just as much sense to stick to the interpretation that Ethan found Lucy dead; the point is that the way the scene is played, it makes just as much sense if you assume that Ethan found her alive and killed her. The interpretation works in the context of the movie and makes Ethan an even scarier character than he already is, because, if you read it that way, he is absolutely deadly serious about wanting to kill Debbie -- he's already done the same to his other niece. I'm not saying that's what Ford intended, but it's part of the fascination of The Searchers: the characters' motivations and even their actions are so murky and hard to figure out that all kinds of interpretations suggest themselves -- and they all work in the context of the story. No other movie makes the audience work as hard to fill in the gaps in the story and the characters, and that's what's great about The Searchers -- it's the original and the best audience-participation movie.