There were several things about ME3 that were terribly executed specifically in the third game, such as:
1. The three endings which were terrible for many reasons, but I won't go into that since the matter has been (and currently is being) discussed quite thoroughly by others. I will simply say they were hugely disappointing, and move on.
2. The fact that they released critical information regarding the origins and, more importantly, the reasonings behind the Reapers as a DLC (Leviathan) which many people (including myself) weren't even aware of because by that point they had dropped the ME series altogether out of disappointment. Perhaps if they had kept that as part of the game, there wouldn't have been so much of a backlash because then at least we would have had some understanding of the troll reasoning of the Reapers.
3. The way that our decisions, many of which should have had a critical impact on the story were dismissed or played down to a laughable angle. I'm thinking specifically of the Rachni quest. The Rachni were a menace, a nightmare, a foe so dangerous that they had to go find the krogan, a species that had not yet discovered space travel, to defeat them. So, I chose to save the Rachni queen, and in the second game we had hints that having done so would have a massive, positive impact on our war efforts. Instead, we had one lousy mission with them, and we never see them again. A huge letdown in my opinion.
And finally, we come to 4., which to me was the biggest disappointment of all (the entire game sucked, but this part specifically): the way they treated our companions. I'm one of those people who gets invested into a series in large by the characters we can interact with, and in the first two games we were presented with an assortment of companions from all different backgrounds that I absolutely fell in love with. Then in the third game, pretty much all of them are treated as unimportant and are brushed aside, having maybe one side mission with them at the most. And God help if you wanted to romance anyone but Liara T'soni, or, horror of horrors, a male character!
I feel like the third Mass Effect game can basically be summed up in "The cake is a lie." We were promised all sorts of things such as a multiple endings (and I believe that there was even a quote where they said "We won't just have three endings"), a satisfying ending to the series, that our relationships with our companions and LIs would have a good impact... and then instead of all that, we got the catastrophe that was Mass Effect 3.
Basically, all of the things which have been mentioned above and in other posts have made lots of players, especially those who played all three games, doubtful of BioWare's ability to do anything correctly when it comes to this series. I feel like a lot of us see Andromeda as their way of trying to capitalize on a once-popular franchise that dove off a cliff and into a volcano, and we're not interested in falling for a bunch of false promises again. I for one will consider purchasing Andromeda ONLY if original players and fans like myself try it and give it good reviews. And even then it'll be with a lot of trepidation. What if I get really invested in the series only to have them pull yet another ME3 on us? Unlikely, yes, but still a sobering thought.