Why is Ant-Man considered part of the MCU?

Ant-Man is a Marvel Comics property. Marvel retained the rights to Ant-Man in cartoon and movie form. That is to say, they never licensed him out, even though there was interest in buying him (from Howard Stern of all people). Marvel Studios, Marvel Comic's movie arm, decided to include Ant-Man in the Marvel Cinematic Universe. That's why he's part of the MCU.

Spider-Man movie rights were licensed to Sony before Marvel ever thought of producing their own films. The X-Men were like wise licensed out to Fox. Including any Mutants, which causes problems for characters like Scarlet Witch and Quicksilver (The Twins in Age of Ultron). So Marvel Studios cannot legally use them in the MCU, without an agreement with Sony or Fox, depending on the character. Many more were licensed out, but most of those have reverted to Marvel. Thor for example, came back in 2006, from Sony, hence Marvel producing the Thor films. Right now, only X-Men (and any mutants, hence Deadpool), Spider-Man, and Fantastic Four are still licensed out.

None of the X-Men, Spider-Man, Fantastic Four, the previous Daredevil 2003 or Elektra 2005 films, Ghostrider, Blade Trilogy (A shame really) or even the upcoming Deadpool films (also a shame) are canon in the MCU. Only films produced by Marvel Studios for Marvel are canon. Notably, Daredevil, the 2015 Netflix TV series, is part of the MCU, as those rights were reverted.

Spider-Man of course, was recently lent by Sony to Marvel Studios, for inclusion in the MCU. Renting a guy their own lawnmower type deal, funny enough.

Because he is a character owned by Marvel Studios and he has interactions with other MCU chracters.

Ant-Man is in the MCU because it was produced by Marvel Studios. Where as Spider-Man (Sony Pictures) and X-Men (Fox Studios) were not.

Within the Ant-Man movie there are references to the Avengers, and even a short fight scene with Falcon (The Winter Soldier, Avengers: Age of Ultron).

Additionally, in the flashback scenes we see Howard Stark (Iron-Man 2) and Hank Pym clashing over the use and appropriation of Pym Particles.

In the most recent Captain America: Civil War trailer we also see Ant-Man gas aligned himself with Captain America's team. Albeit with an upgraded outfit.

Ant Man is part of MCU because he's always been a part of the Avengers storyline:

From the Ant-Man (Scott Lang) Wikipedia page:

Ant-Man (Scott Lang) is a fictional superhero appearing in American comic books published by Marvel Comics. Created by David Michelinie and John Byrne, Scott Lang first appeared in The Avengers #181 (March 1979) and in Marvel Premiere #47 (April 1979) as the second superhero character to use the Ant-Man name in the Marvel Universe.

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And from the Ant-Man (Hank Pym) Wikipedia page:

Biochemist Dr. Henry "Hank" Pym discovers an unusual set of subatomic particles he labels "Pym particles". Entrapping these within two separate serums, he creates a size-altering formula and a reversal formula, testing them on himself. Reduced to the size of an insect, he becomes trapped in an anthill before he eventually escapes and uses the reversal formula to restore himself to his normal size. Deciding the serums are too dangerous to exist, he destroys them.[4] Shortly afterward, he reconsiders his decision and recreates his serums. Pym's experience in the anthill inspires him to study ants, and he constructs a cybernetic helmet that allows him to communicate with and control them. Pym designs a costume made of unstable molecules to prevent bites or scratches from the ants, and reinvents himself as the superhero Ant-Man.[5] After several adventures, Pym is contacted by Dr. Vernon van Dyne asking for aid in contacting alien life. Pym refuses, but is attracted to Vernon’s socialite daughter Janet van Dyne. Vernon is subsequently killed by an alien criminal who teleports himself to Earth, and Janet asks for Pym's help in avenging Vernon's death. Pym reveals his secret identity to Janet, and uses Pym particles to graft wasp wings beneath her shoulders, which appear when Janet shrinks. Janet assumes the alias of the Wasp, and together they find and defeat Vernon's killer. The pair become founding members of the superhero team known as the Avengers.

(Emphasis Added)

Ant-Man is a marvel property, and therefore can be part of the MCU.

We know he's in it though because of his fight with Falcon, who appears in Captain America: The Winter Soldier.

Further, there's the mid-credit scene where Falcon tells Captain America he knows someone who can help Bucky.

It may seem tenuous as the connection was added after the script had been written by Edgar Wright. Here are the details.

It's safe to assume that along with the action and streamlining beats that Adam McKay and Paul Rudd had included in their draft, there's some new characters and ties to the existing Marvel Cinematic Universe. As that was one of the causes that Marvel had cited as relevant in their split with Wright