I hope someone here has encountered something like this and can point me in the right direction...

I currently rent a 1 bedroom apartment (it's basically like a small cottage, it's a standalone building), and the unit came with a God awful 2 burner barbeque (it's useless to cook on, I swear the heat controls barely work, it's all or nothing, even after proper maintenance). I've seen similar models in Walmart for under $100, so you know what kind of quality it is.

I got a new bbq for my birthday, but the Landlord is telling me it's my responsibility to store the bbq that was pre-existing as it "belongs to the property", thus reducing my available storage.

Is it my responsibility to store this old barbeque, or his? If it is, that's fine, but this landlord has a history of doing things or making demands that aren't legal under the Residential Tenancies Act, and makes unreasonable demands left right and center, so I want to be sure before I do anything.

Edit: clarity

Tl;dr; Is it my responsibility to store a barbeque that came with the apartment (replaced with one from my birthday), thus reducing my available storage, or is it the landlords responsibility?