Veronica Khokhlova reports that she is not exactly sure why he wants to resign, but it seems to be about oil.

Roman Zvarych said this on Channel 5 yesterday:

I won’t allow any businessmen, who are also Ukrainian parliament members and hold very powerful positions in the oil refinery sphere, to interfere directly in the work of my ministry. I also won????????t allow the actions and decisions of certain members of the government to try getting members of my family involved in corrupt schemes.

That is rather vague to me as well. But read the rest of her post, as she digs up loads of background information on the events surrounding this.