People are not necessarily upset that they chose to resume the battle (I mean I am, but I definitely do not speak for anyone else). The reason so many of us are upset is because of the cruel treatment of Hau.
Yes, mistakes happen. Nanu is human, and humans make mistakes. The closest comparison I can make to this situation is with the Miss Universe Pageant. Steve Harvey very clearly made a mistake when he announced the winner, that much is clear. The horrible part of the situation comes from the fact that the runner-up was left thinking that she had won for an extended period of time, which made it all the more awful for her when the realization set in that she did not actually win. Yes, it was horrible, but it was a mistake. Everyone agrees that this never should have happened.
The absolutely disgusting part of this is that Pokemon is a fictional show. The writers specifically planned out that this exact situation was going to happen. They purposely let Hau believe that he had actually won for almost two whole minutes. Yes, Hau is obviously not real, but the fact that the writers did this on purpose just for a cheap laugh is just wrong. They could have easily revealed that Rowlet had been sleeping just as Nanu started to declare him unable to battle, but they did not. They purposely chose to go through with this whole thing. They let Hau finally get a taste of the victory over Ash that he had been preparing for for so long just to rip it away from him at the last second. As a joke.