Hard to answer this one.

The triode is a diode with a control electrode (the grid) added.

The only useful answer is that a triode is a voltage-controlled doide.

Try asking the question so that it can be answered more usefully.

a tetrode is used when you need a screen grid tube, but a suppressor grid tube can't be used.

OK, but the question was "why use a tetrode instead of a triode?"

So, the answer...

1. A tetrode has a higher voltage/power gain than a triode.

2. A tetrode has less anode-grid feedback capacitance than a triode, and can operate in common-cathode radio frequency circuits without the neutralisation (or other corrective circuitry) that is needed by a triode.