They say 'You should never burn bridges, even if you want to' and this is generally very good advice. There is a lot to be said for not burning your bridges when you leave an organisation. You never know when you might need to have the help. However, with every good rule there is at least one good exception, in this case I believe there are four or five good reasons to do so.
Burn the bridge with someone who diminishes who you are
There are definitely people out there who will seek to crush your self-worth and self-esteem. They will tell you that without them you will not be able to make it in your chosen career. They will tell you that you'll miss out on amazing opportunities if you go elsewhere. They will endeavour to tell you can only succeed with them. The truth is that if someone is willing to tell you that you're worthless without them then you need to burn that bridge, because it is them who need you, not the other way around. Needless to say the kind of person who purpotraits this type of behaviour is a considerable liar.
Burn the bridge if you might be tempted to use it again
When you work in an environment which is toxic, it is never going to be good for your mental (and physical) health. In situations like this the only real option is to get out as soon as you possibly can. If you feel pressured into staying, it's a sure sign you need to leave. Once you've made that great decision to leave, it's time to burn that bridge. Don't allow financial or other pressures to make any decision to go back into that toxic environment. You wouldn't let your friend go back into an abusive relationship, why would you let yourself back into a work based abusive relationship?
Burn the bridge if you feel ethically or morally compromised
Some people want to silence your ethical or moral positions for financial gain, often not caring for the impact this is or may cause you in the future. You should always be able to stand up for your ethics and morals. If the person who is silencing your ethics and morals, or failing to consider them seriously then you should burn the bridge.
Burn the bridge if that person is a bully
It almost seems like an obvious one, but it's not always as simple as that one. Sometimes this will be a gut instinct, other times you'll feel a bit scared to burn the bridge of a bully. You may feel a bit cautious of cutting out this drain on your resources, but it can be a very healthy and liberating thing to do. Giving time to a bully just feeds their negative force and enforcing that they no-longer have any form of control over you will have new found freedoms for you.
Ultimately, follow your gut
Remembering the phrase 'Never burn a bridge' is a sensible guide for the most part, but as explored above, there are sometimes we need to. If you need to burn a bridge, then you must do it, whether it be vocally, or just to slip away quietly.
When you do make a more vocal stand, you may find you're scared of how you might be perceived. However, generally if you need to burn a bridge you shouldn't give too much credence to that person's opinion of you.