Yes. You can choose. This is one of the very few words in English where you really do have a choice. Both pronunciations are correct. The same goes for 'neither'. Nowadays, as a rough guide, you could say that the British pronounce the first syllable like 'eye', while Americans pronounce it like 'ee'. However, it's not quite that simple.

In the past, the 'eye' pronunciation was also used in the US. There's a well-known American song from the 1930s called 'Let's call the whole thing off', which goes like this:

Things have come to a pretty pass
Our romance is growing flat,
For you like this and the other
While I go for this and that,

Goodness knows what the end will be
Oh I don't know where I'm at
It looks as if we two will never be one
Something must be done:

You say either and I say either,
You say neither and I say neither
Either, either Neither, neither
Let's call the whole thing off.

Over the years, the 'eye' version has largely fallen out of use in the US.

Meanwhile, in the UK, the 'ee' version in becoming steadily more widespread, especially among the younger generation. It's no longer true to say that the 'eye' version is 'what the British say'. Millions of British people do say 'either' with an 'eye', myself included. But millions of British people also say it with an 'ee'.

So, basically, it's up to you. You can use eye-ther pronunciation. Or ee-ther. Whichever you prefer.

There are different pronunciations depending on where a person comes from.You can choose which way you want to pronounce,but you should be consistent and not change the pronunciation all the time.

Sorry. I missed a letter 'o'. You should have said:

'Can I choose EITHER of them...'

I am one of those British people that pronounces 'either' with an 'ee' sound. I just prefer that pronunciation. Likewise I pronounce 'neither' in the same way. It makes no difference, pronounce it whichever way you prefer.

Exactly, pronounce it whichever way you prefer. And just one correction to your post, Addison. You wrote:

'Can I just choose any one of them for pronouncing?'

'Any' is for three or more options. But as there are only <em>two</em> options to choose between, you should have written:

'Can I chose EITHER<em> </em>of them...'  

This, of course, gives you yet another chance to use the word in question!