The only real way to change your cat's (fixed) idea is to either disprove it, or put the cat in a situation where it will prefer to use the door without guidance.
Don't starve, force or hurt your cat.
Sorry about the bolded text, but this is essential. The solutions I'm listing are not intended to mistreat the cat in any way. However, when taken to the extreme, these approaches may become harmful to either the cat or the cat's opinion of you.
Always take a measured approach and use your common sense. Never lose your cool or try to punish the cat. She's only doing what she thinks is right, she's not trying to be a nuisance.
The idea is to inconvenience the cat. It's important that she makes the decision. You can't make the decision for her.
Essentially, you want your cat to think that you're oblivious to the fact that she finds your behavior inconvenient. You play dumb, so that the onus is on your cat to change her situation into one that is not inconvenient to her.
The following are some ideas, not in any particular order.
Treats in front of the door. You've already tried this, but have you tried sweetening the pot? Our cats used to be afraid to leave their room even though they had access to the whole house. One treat would not be enough to get them out the door, but five treats worked. I also noticed that it worked more often if you let the reward grow (treat by treat) instead of immediately giving a pile of treats.
Take a lesson from Scooby Doo (and Shaggy), who usually haggled for more snacks before they would do what the gang asked of them.
Some cats are clever enough to milk it and never come in until they get their bargained amount. If that is the case, once in a while, add a "kill-counter" to your process. Set a limit (e.g. 4 snacks). When that limit is reached and the cat is not cooperating, remove the snacks and walk away. She will learn (after a few times) that she missed out on some snacks by trying to milk it for all she could.
Instead of walking away, when you reach the "kill-counter", you could also simply let her inside without treats. It teaches them the same lesson, they miss out. I think they'll learn faster if you just walk away, but you may prefer a softer approach.
An undesirable guidance from the human. When your cat waits for your assistance, provide assistance in the least helpful way, without scaring or scarring the cat. It's a matter of inconvenience. If you consistently provide assistance in a way that the cat would rather avoid your inconvenient assistance, then she might decide to walk through the door to avoid your unwanted assistance.
In essence, you're trying to convince the cat that it's nicer for her to let herself in, than it is to have you let her in.
- If your cat hates being picked up, pick her up before you walk her through the door.
- If your cat dislikes a certain room of the house, pick her up and take her to that room whenever she needs you to let her in. Be consistent.
- Go sit behind your cat and push her in. Try pushing in a way that's annoying but doesn't hurt the cat (e.g. pushing with one finger = hard poke)
If she's a playful cat, try to see if she breaks her own rules while playing. Get a laser pointer (or any toy she likes). Have her chase it outside, and then have the laser go closer and closer to the door until it's inside. She may be caught up in her hunting instinct that she forgets her own cognitive rules (instincts tends to override cognitive thoughts)
Close the door. Your cat may be indecisive about coming inside (both cats and dogs exhibit such behavior). By limiting the availability of the open doorway, you manipulate your cat into being more decisive.
This is a common marketing technique. Pretend like there's only a few items in stock, and people will be urged to buy one while they still can.
We used to have a cat who would sit by the sliding door, but when we opened it to let her in, she did not move. My mother would leave the door open so she could come in when she wanted. When I was home alone for two weeks, I would give her 10 seconds, then I would close the door and ignore her for the next 10-15 minutes. No eye contact, no interaction. She never really lingered in the open doorway after a few weeks.
The same cat was also indecisive to go outside. She would stand in the doorway, sniffing. I applied the same tactic, the door would only be open for a limited time.
See who's more stubborn, the cat or you? If you never show up to guide your cat, will she stay outside forever? Test it. See how long she's willing to sit by the door. You can remotely interact with her (calling her to you etc.) if you want, but ignore her request for assistance. Play dumb and oblivious.
- Try to see if weather conditions make a difference (rain, cold, ...)
- Don't feel guilty about ignoring the cat. She's in front of an open door, refusing to come inside. Unless she has mental issues (e.g. pathologically fearful) or a bad house situation (e.g. afraid to come inside because of another pet in your house), you can expect your cat to be responsible for its own wellbeing. If it wants to be inside, it should just come inside. Staying outside is a choice that your cat is actively making, and she should bear the consequences of her decision.
Do not hurt your cat. None of these ideas are intended to harm or terrify your cat. The goal of the exercise is to inconvenience the cat, nothing more.
Hurting your cat will make her fear you or become hostile to you, which is not what you're trying to achieve.
Do not force your cat. If your cat fights you in any way, let it do what it wants. Even in the worst case, she'll simply go back to sitting outside and waiting by the door, which puts her back at square one.
Forcing your cat will make her dislike you, which is not what you're trying to achieve.
Do not starve your cat. It's acceptable to let her be hungry (e.g. miss a meal). It's not okay to repeatedly make her miss meals to a point of starvation. If your cat remains outside when she's hungry to an unhealthy degree, this suggests that the cat is adamant about not coming inside, and instead of letting her starve, you should investigate why she is so adamant about not coming inside.