Short answer (again avoiding 5 pages of possibly flameheavy discussion)...
The existing terms, which started with just LGB, describe sexual or gender expression and preference, which ... well, there's no easy way of describing it at 5pm on a friday without offending someone. Let's say it's a mental thing. There's something inside your grey matter that, regardless of what you actually believe is behind it (genetics, chemicals, personal choice, demonic posession...), regulates who you find attractive, and at least some of the time seems to modulate your personality somewhat, generally towards a more androgynous aspect.
Then it became LGBT which also includes another similar "mental" thing - Transsexualism/Transgenderism, or if you want to get coldly technical about it, gender dysphoria. You could argue that this could be seen as the right brain but the wrong body, but at least from a medical and genetic standpoint you have a properly manufactured male or female body, but the brain controlling it has the firmware for the opposite kind installed. Seeing as it's both currently impossible to change the firmware, and would be far more ethically questionable to do so anyway, we do commonly effect treatment for this with physical alterations by way of hormones and surgery. However, a transperson is still a transperson whether or not they're receiving treatment, so physical changes are not the primary indicator.
Now, recently, some have started adding a Q on the end, for "(gender)queer", which basically covers any similar ... ehh... "setups"(?) that don't quite fit those slots - neutral/third gender, asexuality and so forth.
And the acronym is already getting a bit unwieldy.
Putting I on the end is arguable; it both seems sort of fair and a sensible extension, but also it changes the game somewhat. An intersex person is not necessarily expressing a non-"straight" (within the majority heteronormative social mainstream) gender, sexual preference or even sexual identity, but does have a non-binary sexual phenotype. A non "straight" physical expression if you like, and most certainly not one of choice even if you were operating from that standpoint for the others. EG an individual with an XY genotype, male gender identity and a sexual preference for women... with micropenis or hyperspadias, which is an intersex condition, although often only a mild one. Or man-preferring XX female with clitoromegaly (staying within the purely genital area which I know is an oversimplification, but roll with it). The line is a little blurry now... where do you draw it?
How many more letters are there to add?
Seeing at least what's on the first page, and thinking about this, I think I fall into the "need to rethink the collective noun to make it more inclusive" camp... Give emphasis to the idea that this sort of thing isn't really an "either/or", but more of a spectrum, as per the theories of ol' Dr Kinsey and plentiful pyschological, physiological and genetic research since. There may be some distance in "reclaiming" Queer, for example, but that may be "too soon" and open to abuse (given that Gay and Lesbian were themselves at one time obscuring euphemisms, rather than ubiquitous homonyms for male and female homosexuals)... and it still may put too sharply defined a bar between the dead-straights and anyone who feels they want to claim that badge for themselves.
Difficult. Very difficult. But the tl;dr version as to why LGBT hasn't habitually become LGBTI (yet) is that the first four represent psychological aspects, your mental workings and personality, which are maybe easier to hide from cursory examination but hellish to withstand, and the latter is more of a traditional physical determination, which is clear for anyone to see if they whip your pants off but otherwise doesn't explicitly affect who you are mentally. It's maybe an abitrary distinction, but it's a distinction nontheless.
