Particularly children with their parents, if a persons small everyday issues are ignored, dismissed talked over, then this can leave a person feeling alone, abandoned, rejected or feel they are a burden or inconvenience, or that what they are trying to share is somehow not acceptable. Imagine what bigger problems this can lead too in the long term!
They can become withdrawn, isolated, distrusting of people, low self-esteem and confidence. They come to learn they should not share or express themselves and so turn their feelings inwards or explode outwards leading to mental illness. They don't learn to be resilient with their feelings because they are busy trying to 'get rid of them' because they aren't supposed to have them and so develop anxiety and feel overwhelmed.
It may take conscious effort but when somebody seems to be wanting to share something with you, just pause for a moment, long enough to stop and listen to it without intervening and without comparing to yourself. Offer something back that indicates you have heard them such as making eye contact, stopping what you are doing and looking up, saying something like "I can hear this is really worrying you" or even "I can understand that".
Two Way conversation can be hard when both parties are invested and it can get carried away when both want to be heard. The energy can escalate when neither is listening properly and each person gets equally frustrated. So even though you want to be heard just take a pause of your own thoughts before speaking and pay attention to the other person.
Don't be scared to challenge somebody who doesn't appear to be listening. Ask them if they are listening if you are not sure. If they insist they are but you are still not convinced tell them what you are experiencing that makes you feel you are not being listened too ie; "How are you listening if you are now talking about the task you are now doing?" .