The usual version of this question sets a rent against a mortgage payment and declares the smaller one the winner. That comparison is wrong on both sides, and correcting it changes the answer often enough to be worth the trouble. This page describes the arithmetic and the terms of each tenure; it does not recommend either.
Why the usual comparison fails
A mortgage payment is not a cost. Part of it, the repayment of principal, is a transfer from one pocket to another: the money leaves the current account and reappears as a reduced debt. Counting it as an expense overstates the cost of owning.
At the same time, ownership carries costs that no payment shows: property tax, insurance, maintenance and eventual replacement of components, any association dues, and the transaction costs of buying and later selling, spread over however long the house is held. Ignoring those understates the cost of owning. The two errors run in opposite directions, which is why the naive comparison can land anywhere.
Stating it properly
The honest comparison is between the rent paid and the true annual cost of owning the same house: interest actually paid, plus tax, insurance, maintenance and dues, plus the return foregone on the money tied up in the deposit and in the equity accumulated, minus any change in the property's value over the period.
Set out that way it becomes clear why the answer is local and time-dependent rather than general. The relationship between rents and prices differs by neighbourhood and by property type, the return foregone on capital depends on prevailing rates, and the transaction costs are amortised over the holding period, so the same house can favour renting at three years and owning at twelve.
What each tenure actually buys
- Renting buys optionality. The ability to leave at the end of a term, at low cost, is worth a great deal to a household whose work, size or preferences may change.
- Owning buys control and duration. The right to alter the place, and security against being asked to leave it, are the two things renting structurally cannot provide.
- Renting transfers risk. Maintenance, major replacement and the property's value are someone else's problem.
- Owning is a forced saving. For many households the repayment of principal is the only saving they reliably do, which is a behavioural argument rather than a financial one, and none the weaker for it.
The part that is not arithmetic
A house is also a place, and the value of staying somewhere long enough to know it is real even though it does not appear in any calculation. Schools, neighbours, a route to work and the accumulated knowledge of which shop opens early are all forms of capital that renting can hold and frequent moving destroys.
Equally, the freedom to move for a better opportunity is worth something, and households that over-weight ownership sometimes purchase immobility without noticing they have bought it.
A note on framing
Both tenures are ordinary. The rhetorical framing of renting as money thrown away, and of owning as an automatic route to wealth, describes a particular historical period rather than a law of housing. The arithmetic above is neutral and will return different answers in different decades, which is roughly what one should expect from an arithmetic.