Why can't I make vegan mayo at home?

Answer 1

The problem is you need an emulsifier to get oil and water based ingredients to mix and stay mixed. In the regular recipe this emulsifier is the egg yolks which you can't use in vegan food,

Here is one recipe that should work:

Combine soy milk, lemon juice and mustard in a blender or with a wand blender for about 30 seconds. While blending, slowly add in the oil until emulsified and it thickens. Add the salt and pepper and blend.

In this recipe the emulsifier is the soy milk, it isn't quite as effective as egg yolk so you will have to be more careful to avoid "breaking" the mixture.