There's a couple circumstances where having both loans and savings makes sense. One, emergency fund - if you have a $3000 problem with your car, you can't pay your mechanic with your lack of a mortgage, you need cash. Having to go get a loan at that point isn't really practical. If you have revolving credit(credit card/line of credit) then you can use that, but a traditional loan that goes away when it's paid off is no good.

The second case is leverage loans. When you borrow for business purposes, the interest can be used as a tax deduction(in most countries, consult local tax advice before trying to do this). Depending how you invest, you can get tax-advantaged returns in the form of dividends and/or capital gains, whereas the loan is a tax deduction at ordinary income tax rates. In Canada, capital gains are taxed at half the normal rates, so if you borrow at 4% and earn 6% of capital gains, you're getting a deduction of 4% of the loan but only paying tax on 3%, so you pocket a net tax deduction of 1% of the loan size, on top of earning a spread of 2%. All this without putting any of your own money in. That said, this is a higher-risk strategy, because if you lose money you still need to pay back the loan, so it's not for everyone.

The third reason is psychological. Some people believe that you should make a habit of savings. Depending on who you are personally, it may be a decent tactic.