This whole case seems so odd. As somebody pointed out earlier in the thread, we don't even know where Charlotte went missing from. On the facts we have, there are three broad scenarios with numerous possible 'subscenarios' (for lack of a better word!).
Scenario 1 - Charlotte makes it to the airport on 1 Sept 1972 and boards the flight to Michigan
If Charlotte made it back to Michigan then something would have had to happen to her almost immediately on her return - nothing else explains the luggage left at the airport. The likelihood of a stranger harming her in this scenario seems very slim - it would have had to have happened between the flight landing and the luggage being collected, given that she apparently never got her luggage.
If it wasn't a stranger, that leaves her family. We don't have much info in this case, but how was Charlotte going to get from the airport to home? Were her mother and step-father or another sibling picking her up? If a family member collected her then why was her luggage uncollected? The only explanation for her luggage being left at the airport in this scenario is that a family member returned it to the airport after harming Charlotte in some way but why go to the trouble and risk? A far easier explanation would be to say that they went to collect her but she and her luggage had gone and imply that she had run away.
Scenario 2 - Charlotte makes it to the airport on 1 Sept 1972 but never boards the flight to Michigan
In this scenario something has to happen to Charlotte during the short period between her arriving at the airport and the flight leaving without her. Either she doesn't catch the flight of her own free will to run away or somebody stops her from catching the flight (kidnapping and murder) but neither of these are plausible. Firstly airports are hardly ideal locations to kidnap teenage girls - they're full of witnesses and a teenager is not going to go quietly with a stranger if she doesn't want to, and why would Charlotte want to?
It is possible that Charlotte ran away and used the trip back to Michigan as the opportunity, but why? If she didn't want to go home that badly, why not tell her sister Carole and ask her if she could stay? Why check the luggage onto the flight - what, if anything, would she have had with her that wasn't in the luggage? Did she have any money and if not, then what was she going to live on in the short-term? If the motive for running away was to avoid returning home to Michigan, perhaps because of her step-father, why has she never got in touch with any of her surviving siblings? Why has she never used her Social Security number? Why hasn't she been found in the intervening years by the police, even if just to tell them she's safe but does not want her family to know where she is?
Scenario 3 - Charlotte never goes to the airport on 1 Sept 1972 and therefore likely never leaves New Jersey
The most likely scenario in this case is surely that Charlotte never left New Jersey. Did anybody see Charlotte go to the airport on 1 Sept 1972, other than (presumably) Carole and Alvin Fleming? If not, then it is only their word that she did, which leads to the question of when was Charlotte actually last seen or heard from other than by Carole and her husband?
In this scenario Carole and Alvin Fleming would have had to have lied about Charlotte going to the airport to catch a flight home and if they lied, then you have to ask why? Obviously somebody went to the airport that day and checked Charlotte's luggage in but if not Charlotte when her sister says Charlotte went to the airport, then surely it must have been Carole or Alvin, which of course leads to another why and, in my opinion, two 'subscenarios'.
First, Carole says Charlotte went to catch her flight back to Michigan when she didn't in order to protect her from someone by letting her stay in New Jersey without anybody realizing and trying to bring her home. Honestly, I find this highly implausible. If Carole was concerned enough to go to these lengths, then surely she would have either contacted the police or insisted that Charlotte stay with her. In any event, at some point this lie would surely have become unnecessary and doesn't explain why Carole never told anyone or why Charlotte has never contacted any of her other siblings, used her social security etc.
Second possibility, something happened to Charlotte that prevented her from leaving New Jersey and her sister and/or brother-in-law lied to cover this up and checked in the bag to make it look as if she arrived at the airport as planned. Again, it would be great to have more information on this, like who supposedly took Charlotte to the airport etc. but I guess at this stage we probably won't ever know the details.
It's a shame that so little was done at the time because so much evidence will have been lost which would have thrown so much more light on everything. Airport staff and flight attendants could have been interviewed, passenger lists considered, Charlotte's luggage could have been looked at. It could have at least been determined where she went missing if nothing else. All of these opportunities have gone now.
Anyway, sorry for the novel of a post! These all just theories and opinions from reading the thread and the very little info out there on Charlotte's disappearance. Short of a body being found or Charlotte miraculously coming forward, I don't suppose we'll ever have an answer to this. So many of the key people are now dead that a murder confession is highly unlikely.