Concerning fate of Milky Way Galaxy Andromeda Galaxy is the largest galaxy in the galaxy cluster[1] called Local Group[2] and our Milky Way Galaxy as well as some satellite/dwarf galaxies are orbiting around each other within Local Group. My question isn't Milky Way Galaxy supposed to orbit around Andromeda Galaxy[3] so how come the predicted merger[4]? Whose slowing down or do the gravity work differently as things are being scaled further up?
The Milky-Way does not orbit the Andromeda galaxy, they both move under the influence of all the members of the local group. Even if one were orbiting the other the orbit need not be near circular but could be a very eccentric (elongated) ellipse.

The projected merger is because the tangential component of Andromeda's velocity with respect to the Milky-Way is small compared to its radial component That is Andromeda galaxy appears to be moving almost directly towards the Milky-Way (which is what it says in the Wikipedia page you link to, but it is not too difficult to find primary sources using Google, here is an arXiv paper reporting a proper motion study of Andromeda and reporting such).