It's supposed that they are in a relationship and Modest! management hides their real sexuality by creating "beards" like Eleanor Calder and Taylor Swift.
"Beard" definition: "Slang a woman who accompanies a homosexual man to give the impression that he is heterosexual" (http://www.thefreedictionary.com/Beard)
The reason why Louis "denies" the romance is because Louis earlier said to Harry that it would be HIM the one who will lie and face everything about their secret romance just to protect Harry, so Harry won't have to lie about it.
But... Louis has NEVER EVER denied Larry, if you look for the interviews where he talks about Larry, he often makes jokes about it, (a liar feature), but never denies it.
Let's talk about what Modest! Management does about Larry. Usually management makes Louis do something to confirm his heterosexuality—like go out with Eleanor in public—after a Larry moment happens.
Now, let's talk about the Tweet, William Beckham (@Will_Beckham) is a Louis' old friend, and he has said by his Twitter account this:
"@Louis_Tomlinson "you" have tweeted many atrocious things in the past year, but that has unquestionably beaten the lot... i don't often comment on One Direction anymore, but - the idiocy
of Louis and their management is utterly staggering."
So, Will have confirmed that Modest! can Tweet anything they want to by Louis' account (not only Louis' account, a long time ago Liam was waving a sign at fans when "he" replied to those Larry tweets. Fans SAW HIM THERE. He wasn't online). Also, during a tweet cam less than two weeks ago, Louis was asked why he blocked someone on twitter. He replied: “I’m not sure I did to be honest”
So, basically, Louis wasn't the one who replied that Tweet, he wasn't the one who called Larry "the biggest load of ???? I've ever heard."
Now, WHY LARRY CAN'T COME OUT?
Basically, because if Larry comes out, lots of things would happen:
1. Millions of fans would do crazy things (suicide) because of "the love they feel for Harry or Louis" (most of them are "in love" with Harry)
2. One Direction would become "the band with two gay men in it", so people would focus on them, on HOW did they know each other and things like that, and obviously, Zayn, Liam and Niall would stay "under the shadow" forever.
3. We're talking about men who are "reachable", it gives fans "a hope they can marry them one day", but, if Larry COMES OUT, there wouldn't be THAT hope for them.
4. There are fans who are still blind, and think "the boys wouldn't ever lie to us", if Larry comes out, they would feel "dissapointed" and obviously won't but their CD's anymore.
5. Some parents wouldn't let their children listen to "gay music".
So basically, it would be a LOSS OF MONEY, and that's what Management is afraid of, and those are the reasons why Harry and Louis can't come out as a couple, because they have to THINK about the money, about the fans, about their family (Louis' little sisters don't know anything about Larry), about Liam, Niall and Zayn, because they have to think about lots of things before that moment happens, because they have to lie, because they have to hide their love, because they have to be BRAVE to face lots of things.