a thick/thin skin
The ability to ignore verbal attacks or criticism from others. If you're going to pursue a career in politics, you're going to have to develop a thick skin and not let the criticism of your detractors bother you.
Insensitivity to criticism or insult, as in You can tell him exactly what you think of his new piece; unlike most composers he has a thick skin . This term transfers an impervious outer coating to mental or emotional toughness. [Mid-1500s]
a thick skin
COMMON If someone has a thick skin, they are not easily upset or offended by criticism. To survive in politics, you need a thick skin. As a salesperson, you have to have a thick skin to deal with all the rejection. Note: You can also describe someone as being thick-skinned. She's so thick-skinned, she won't even have noticed the insult.
a thin skin
COMMON If someone has a thin skin, they are very easily upset or offended by criticism. He'll never make it in journalism with such a thin skin. Note: You can also describe someone as being thin-skinned. She didn't mean it as an insult — you're too thin-skinned!