Feeling value system rigs one's brain for cooperation within one's species. It places a lot of value on other people and less value one oneself. As a result feelers may lack confidence and experience feelings of low self worth, however they will have increased interest in other people and relationships in general, more acutely aware of worth of others, more sympathetic and desiring to seek win-win situations rather than win-lose competitive situations. Competition is distasteful to F-types. Most of women test as F-types as well as about 20% of men. F-types with tertiary T-function will find it easier to access T-type logic.
When decision stands to be made, our judgement function can reference either T or F value system. The two value systems, however, are inherently incompatible. When the feeling value system has been crossly violated, this sensation to us is known to us as guilt. When thinker value systems has been violated, this sensation is known to us as lack of respect, disdain. Not surprisingly it also plays into misunderstanding across genders. Unlike the N and S divide, or the I and E divide, this divide does actually correlate to gender and is responsible for the famous "men are from Mars, women are from Venus" saying.
What happens if you don't process your feelings is that you may either completely reject them and use pure T-type logic in relations to other people. This can harm your relationships as you will start acting selfish, callous, and cold towards other where other type of behavior would have made all the sense. And on the other extreme if you don't take time to process your emotions this may lead you to act in a way that others will simply take advantage of you. You will be cooperating where you should have been competing, so once again it can harm you.
So anybody gives you problems and belittles your emotions - give them this little lecture :P Emotions are in fact a very powerful tool that keeps the society together. If people went around not processing their emotions the world would be much more of a mess than it is now.