I'm far from being an archaeologist, but I tried to follow the various positions re: the sky disc for some time and hope to be able give you at least a starter on a) why there were doubts on its authenticity and b) why current scholarly consensus is pretty firmly in the "it's real" camp.

Re: the first point, the entire thing begins with two unlicenses treasure hunters digging around on the Mittelberg mountain in southern Saxony-Anhalt in 1999. The two diggers found the disc using a metal detector together with two bronze age swords. Not only did they manage to damage the disc while extracting it (one of the stars fell off), they also knew fully well that what they were doing was illegal, as the state of Saxony-Anhalt claims all treasures found in its territory for itself. The day after they found it, they sold it off to a fence in Cologne for 31,000 DM. For three years the disc changed possession several times, but after a while word got out that it did in fact belong to Saxony-Anhalt (which made it worthless for legitimate art dealers). The state archaeologist of Saxony-Anhalt, Harald Meller, realised the possible value of the objects and organised a sting in 2002, in which he met with the current owners who in turn were arrested by the police. The authorities managed to trace back the disc's various owners all the way to the original diggers, who showed Meller the exact spot where they found.

And right there there's the first and possibly most important reason for why doubts about the disc's authenticity were able to come up in the first place. Besides it being found by two random guys with detectors instead of being unearthed by archaeologists as part of a properly documented dig, the fact that all treasures found in Saxony-Anhalt automatically belong to the state means that if the diggers and the other various fences and owners throughout the years were able to prove it being fake, the whole case against them would fall apart. This is why eventually it needed a court deciding that the disc was in fact genuine, and why the legal defence team of the accused tried to stir up as many points of doubt as possible.

In addition, a find of this magnitude means that almost automatically conspiracy theories and similar spring up like mushrooms. A couple of years ago, the museum keeping the disc complained that almost every day they got another call by some weirdo claiming that they found the disc in their attic, or that it was beamed into the ground by aliens and so on. The importance of the object also provoked a lot of professional jealousy. The most (in)famous case of this probably is Peter Schauer, a renowned archaeologist at the University of Regensburg who apparently had some private beef with Meller and wrote an angry letter to a national newspaper in which he doubted the disc's authenticity for several reasons, all of which were later determined to be baseless. Schauer later had to admit that he never actually had seen the disc in person and only knew it from photos.

So, those are the main reasons why people claimed and still claim that the disc is fake. But why is the vast majority of scholars reasonably sure that it is instead the real deal?

If you want to read up on the arguments for it being genuine yourself then you can do so here. The site belongs to the state archaeology office of Saxony-Anhalt, however, so you can fact-check their arguments against those made by people who don't have a vested interest in its authenticity if you want. Personally, I think their arguments are perfectly sound and I'll summarise them here:

1. By measuring the amount of Pb-210 isotopes in the metal you can prove that it must have been smelted at least 100 years ago. Scientists weren't able to determine any amount of Pb-210 in the disc, which in turn means that its metals must have been smolten during the 1890s at the latest. It would have been possible for forgers to use older metals for a fake disc, but the possibility of measuring Pb-210 to determine a minimum age only was discovered after the disc was found, so this doesn't seem especially likely.
2. The disc shows corrosion fitting perfectly to what would have been expected after lying in the ground for 3,600 years (the determined age of the disc according to the soil layer it was found in). While it would be possible to fake this corrosion, it would have been extremely difficult to do so.
3. The bronze and gold alloys' composition in the disc perfectly fits comparable alloys of the bronze age. A forger trying to emulate this would either have to melt down other bronze age originals or dig up gold nuggets from the appropriate regions.
4. Trace amounts of soil adhesions on the disc perfectly match both the spot and the layer where the treasure hunters claimed to have found it. By my understanding, this is basically impossible to recreate by artifical means, as the adhesion is the result of a process taking several centuries.
5. In the hilt of one of the swords, remains of tree bark were discovered which allowed for a C-14 measurement. Since the soil adhesions firmly point to the disc being of the same age and location as the swords, it stands to reason that the measurement's result of the bark dating back to the period between 1650 and 1500 BCE would also extend to the disc itself.

I can't say why your friend claimed that most archaeologists still doubt the disc's authenticity, but by my understanding as someone outside of the discipline this doesn't seem to hold true. Instead, the consensus seems to be that it is in fact genuine. Extraordinary claims - or in this case, rather: extraordinary discoveries - demand extraordinary proof, but I think that this proof can easily be provided for the disc.