It's not arbitrary but it is personal preference. You don't need multiple oils, soap can be made with just one type of oil, lye and water. Castille soap is just olive oil, lye, water and nothing else. Each oil does have it's own properties and that is why you'll see soaps made with multiple oils. Only certain oils will make your soap hard as a cured bar. These include....
Olive oil - although it can take up to 6 months to cure if used on it's own
Coconut oil
Palm oils
Tallow
Vegetable butters
The other oils are known as soft oils and if used on their own won't make a hard bar of soap. So if you prefer soft oils like rice bran, canola etc, then you will also need to include some hard oils (usually about 30%) in order to make a bar of soap that cures nice and hard. Everyone tends to settle on a mix of oils that they think makes a nice bar of soap, this differs from person to person and their goals in soapmaking.
Each oil behaves differently in soap. With their attributes classified like this...
Lather - how much and what type of suds it produces
Hardness - how it cures
Cleansing - how drying the bar will be on the skin
Emolliency - how softening and soothing it is
I make what I think is a very nice soap with just 2 oils. If you are just starting out find a recipe that's as simple as possible. It will be easier to learn with and also cheaper since you only need a few ingredients. You can always change your recipe on your next batch. Here's a link to an article listing all the different types of oils and how they affect soap.
http://summerbeemeadow.com/content/properties-soapmaking-oils
For a very basic understanding..
Coconut and palm oil are usually included because it creates lots of suds and makes the bar hard. They are necessary if you want to make an all vegetable oil (non castille) soap. They are also drying on the skin so most people keep these oils less than 30% of the recipe.
Tallow makes a very hard bar that's also soothing on the skin but it has few suds (people with an objection to animal oils also don't want to use it, its beef or pig fat). Coconut oil and tallow together will make a hard bar, that's soothing and has suds.
Castor Oil is usually added (5-20%) because it improves the lather of other oils and is very soothing on the skin. But it makes soap soft.
Olive oil is a favourite of a lot of people. It makes a hard bar but few suds and takes a long time to cure. Olive oil lovers often make soap with olive and coconut oil to improve the suds and cure time of the bar. These two oils together make a nice bar. If you want an easy recipe in an all vegetable oil soap this is a pretty good combination to choose.
Vegetable butters are quite expensive so people usually only use them in small quantities (10-20%) in the soap for their skin softening properties and ability to harden the bar. They are by no means necessary and are a bit of a luxury item.
Traditionally soaps were made with either 100% tallow or 100% olive oil. So this modern day malarky of choosing many oils wasn't a concern. However choosing many types of oils makes the hobby fun.
