'[C]onverse' effectively means 'the opposite'. Therefore you can use 'the reverse' in more or less the same way as 'the reverse' when discussing a topic that has both good and bad points. If you're not sure when to use 'the converse'/'the reverse' see if you can write the opposite statement instead.
'Building new roads increases traffic. Not building new roads increases traffic.' So using 'the converse' is a shortcut implying the negative without directly saying it.
You'll often find the word 'conversely' used to introduce an alternative side to something. Note: it's usually used to imply a negative, but not always, and you have to state the opposite point as well.
For example, 'English is a very useful language if you want to travel, conversely it might be difficult if you're a native English speaker who travels because people could want to speak English to you rather than their native language.'
Hope that helps.