The southern states wanted to break away from the northern states because they wanted preserve the institution of slavery and wanted it to be legal and the north opposed it. The south wanted to break away so they could be their own country that allowed slavery. No they were not right because slavery was wrong and the southern states signed the Declaration of Independence agreeing to be apart of a country with the north. That does not give them a right to break away and become their own country.
Hope this was helpful :)