I solved my problem. The problem is loading Twitter auth page.
When I use this I get "wrong username or password" error:
webView.postUrl("https://api.twitter.com/oauth/authenticate?oauth_token=aaa123",
EncodingUtils.getBytes(data, "base64"));
I don't get this error for this type of call:
webView.loadUrl("https://api.twitter.com/oauth/authenticate?oauth_token=aaa123");