Why are some people unable to go to an event without alcohol.
What a strange question. The answer to which can only be that they are alcoholics.
But the point is that the Horniman is not going to make alcohol compulsory for all events or visitors to the park, the question is should alcohol ever be allowed to be served/sold in the park, and if so under what restrictions.
Many other museums in London are able to sell alcohol in their restaurants, there is no reason why Horniman should not be the same.
Personally I have enjoyed many happy weekend afternoons in the park with a bottle or two of wine. I find it particularly enjoyable to soak up the sun, listen to the music drifting across the park, chat to friends, and have a glass or two of wine with some strawberries. I'm sure you'll agree that it sounds like a lovely summer afternoon.
I'm not unable to visit the park without alcohol, but occasionally I like to, and I don't see why you want to stop me.