Why was it difficult for Emily to meet suitable men in her youth?

I am going to take a guess here and assume you are asking about Miss Emily in "A Rose for Emily" by William Faulkner.  The answer to your question is found at the end of Section II. where we are told, "We remembered all the young men her father had driven away,..."(290).  There are a few inferences we can draw from that statement, one being that her father might not have considered any of the young men "suitable," and another being that he was selfish and wanted to keep Emily at home to take care of him. 

Another aspect that you might want to consider is the time during which this story takes place.  World War I was likely to have eliminated many eligible men, and the Depression is likely to have made many men financially "unsuitable," even after Miss Emily's father dies.

Additionally, given the setting of the story, a small Southern town, it is likely that there were few if any men whom either Emily or her father would have considered worthy of the daughter of a clearly wealthy man.

I hope this helps.  Good luck!