Guilt and Giving - Use of Faulty Logic

This is true since when we let x=1 we get
1² - 3(1) + 2 = 0, which is true.

This is what is known as the inverse of the statement on the left.  In the inverse, both the if-part and then-part are negated. Often, as is the case here, the inverse will not be true even though the original statement is true. This statement is false since the number x=2 is not equal to one and it is a solution to x²-3x+2=0.

I think we can all accept this statement as being true, at least on an individual basis.  It is true that corporations will often raise money for children's causes to generate good PR, but we will restrict this to individuals to avoid that case.

Often, this is the type of "guilt trip" suggested by phone solicitors when you fail to make a donation to their charity. They are hoping that since you believe that the original assumption shown on the left is true that you will automatically assume that the inverse is true.  When we (falsely) make that assumption, then we start feeling guilty and may donate.  After all, who wants to not care about the welfare of children?

The fact is, however, that you do not need to donate money to that particular organization to care - you can show your concern in many other ways.