I don't get it.

Same here... Is anyone care to explain?

The constant conflict between these lovers of each snacks is called the Kinoko-Takenoko War.

See Nicopedia and pixpedia (JP).

EDIT: This is one of two major food conflicts of Japan. The other one is 'the Great War between Akai Kitsune and Midori no Tanuki.'
The Nicopedia article is here.

So basically Mami and Homura are trying to forcefully feed each other their love of those snacks.

henmere said:
EDIT: This is one of two major food conflicts of Japan. The other one is 'the Great War between "Akai Kitsune" and "Midori no Tanuki.'"

It is funny to see the two sides involved in both wars come from the same manufacturer, Meiji and Toyo Suisan (i.e. Maruchan) respectively.