You probably cannot refuse to get mortgage insurance and still get the loan you want from the lender. Most lenders are requiring mortgage insurance if the buyer is not putting a 20% down payment on the property.
The requirement for mortgage insurance is a result of the housing market cooling and the lenders reassessing how they loan money. In this tightening market the free-form creative financing that was available a few years ago has dried up. First-time home buyers, those with credit flaws, and those with small down payments who are correctly selecting the conventional fixed rate mortgage are being directed to a fixed rate mortgage backed by private mortgage insurance (PMI).
The PMI is paid for by the borrower as a monthly fee. Your mortgage lender will probably include this in your monthly mortgage payment as your property taxes and house insurance already are. The PMI monthly fee is typically a set percentage of the total mortgage loan. If in the future you are unable to repay the mortgage loan, then the lender is assured of getting some of its money back. It is a way for a mortgage lender to be secure in loaning money to a borrower who may not qualify under current guidelines.