It is true that the behaviour of a cat would be at least 50 per cent down to the influences of the environment she grew up and the one she now lives in. A timid born cat if she is living among other pets and people she will eventually become a lot more confident than she would have been if she was living on her own with only one human carer. The same applies to cats that they might have shown traits of exploratory behaviour and were also shown to be in general rather extrovert and although in their home environment they might appear to be brave, curious and in some cases a bit of a bully when strangers are visiting their house or when for an example an opportunity appears for them to explore unfamiliar territory they will quite possibly show an unexpected timid behaviour and they will more likely go into hiding or they will simply refuse to explore. These are behaviours which the cats have learned under their current living environment. But of course these types of cats that they have already the traits of being rather fearless are much easier to train to overcome their fears than cats who are timid by nature as they are going to be rather conscious when it comes to any kind of changes.
Of course fear and weariness of anything new and unfamiliar it is a natural trait for predators small as the cats and vulnerable to other larger and more dangerous ones, a trait which they need if they are to survive. This is why quite often cats that they are rather scared of people and other pets and who spend considerable time outside tend to survive longer than the ones that they are very friendly and trustworthy. In which cases it might be better if the cat is going to spend time outdoors then not to be trained to lose all her fears if possible. A bit of aggression and defensiveness might be required for survival.
As cats are generally weary of changes and other pets invading their territory it isn't also unusual to have regular confrontations with the new member cat and often to take a long time for one cat to get used to another. Cases of cats that they finally learn to tolerate the presences of other cats vary from one month to two years plus. Cats that they grew up in an environment in which only humans were around find it really hard to accept another pet in their territory as quite often have a difficulty to understand the other pet's body language. So while the other cat might be inviting the older cat to play, the older cat then wouldn't find really difficult to understand the younger's cat body language and as a result she will more likely interpret it as an imminent threat and she will then try to defence herself. Those cats that they have not grown up among other cats are more likely to understand better humans' body postures and even human voice tones than other cats. So this is why introductions and acceptances in such cases take a long time, the cat needs not only to protect her territory from a new unknown cat but also to make sense and communicate with that cat, she has to learn more or less a new body language.
Unfortunately in many cases humans seem to run out of patience and to expect things to settle down in a few days and the two cats to become the best of friends in a very short period of time. But of course this doesn't happen with many cats as some cats are more trustworthy, friendlier and have perhaps lived with other cats and have learned the important body language while others are the totally opposite and therefore they will as a result require a longer period to trust and understand.