Career is defined by the Oxford English Dictionary as a person's course or progress through life ( or a distinct portion of life ). It is usually considered to pertain to remunerative work ( and sometimes also formal education ).
What convinces is conviction. Believe in the arguement you're advancing. If you don't, you're as good as dead. The other person will sense that something isn't there, and no chain of reasoning, no matter how logical or brilliant, will win your case for you.