Many people have sensitive skin specially in their hands.
This is usually caused by exposure to different chemicals when doing housework: dishwashing liquids and other cleaning agents can cause this.
This is why you should always use latex gloves when you are handling such chemicals - you can avoid getting sensitive skin by protecting yourself.
For this reason in a lot of different professions it is required for latex gloves to be used during working hours.
Hairdressers for example are using strong chemicals and oxidants during the dying process, and when doing a perm for the client.
Numerous hairdressers get allergic to these chemicals and have to stop working, even if they are using the necessary protective equipment.
The chemicals that are used in washing the dishes and cleaning the house are designed to remove fats from the area where you are using them.
When your skin is in contact with these chemicals, the protective lipids in it are removed and the harmful chemicals can readily penetrate the skin and cause severe reactions.
This can easily be prevented by using latex gloves while doing these chores, and if you are allergic to latex you can always use nitrile gloves - they are more common in laboratory work because of their strong resistance to acids.
Besides just giving protection from chemicals, wearing gloves will help you avoid those small cuts that you get on your hands easily when cleaning up the house.
Protection from chemical and physical dangers should be enough for you to consider wearing gloves more often.