Why IE and Firefox don't share the same border width when creating html?

Because they are different.

Different peoples interpreted recommendation with different point of view and used different approaches to integrate them in different libraries.

That and because IE is so flawed, that it's an impossible mission to correct it now without breaking 10 years of bad web coding.

So this means that will be always mess with it couse sometimes the whole div is disrupted. IE shows border:2px and firefox 1px. Small detail but hard to handle with it.

Firefox and IE both understand 1px vs 2px.
What is the code you're using to specify the borders?

It sounds like you're doing something else to me, too.

Where's the page that the offending code is on?

Something tells me this is going to be about IE's interpretation of the box model.

Could you post the code you're using. It will help us determine what the issue is and help find a solution for you.

I dunno if you know this or not but, sometimes it helps putting this code in youre css style file:

/* Basic arangement */
html {  padding-bottom:0px;
		padding-left:0px;
		padding-right:0px;
		padding-top:0px;
		margin:0px;
		
}
body {	padding-bottom:0px;
		padding-left:0px;
		padding-right:0px;
		padding-top:0px;
		margin:0px;
}

The padding on html is not necessary.
That whole mess can be shortened to this:

body{margin: 0; padding: 0;}

However I rather doubt that padding has anything at all to do with the border issue.

I don't think the issue is in the code you posted. If the page is online could you post a link to it? I not could you post all the code?

You might want to read this. I think it's what you're having trouble with.