Here's what that actually says:
View attachment 121198
I think there's a lot of room between the 3 official bullet points and the additional design intent section that was posted for curiosity.
As usual the Sage Advice speaks in riddles.
Looking at Twinned Spell, we see that this ability can be used to get close to casting 2 non-cantrips in the same round: if you have 2 slots of a certain level X, you can "burn" one of them as a bonus action to get the X sorcery points required to use Twinned Spell on the other slot.
There are already some obvious caveats, first of all they have to be
same spell, but then technically they are really just 1 casting, so among other things it takes a single counterspell to stop them.
So probably the first
intent is to simply limit the general usefulness of Twinned Spell to make it less likely that a Sorcerer uses it every single round, consuming her slots at double speed to cast 2 spells for the whole battle. So they put more limitations on which spells you can use it with, but at this point which spells to ban is still arbitrary (for example, they could have said "you can't Twin spells of your current highest spell level", or forbidding concentration spells or spells longer than instantaneous...).
But the second
intent is probably for playability's sake to avoid Twinned Spell to cause too many rolls at once. That's why you can't Twin area spells, otherwise you might trigger a lot of saves (notice that perhaps for the same reason they did not design a metamagic which e.g. doubles a spell area).
Why then no "self" spells? Most self spells don't stack with themselves or simply don't make sense to cast twice anyway. However,
some self spells are actually... area spells! For example Lightning Bolt or Prismatic Spray. Basically if the "area" starts from the caster, the spell usually has Range: Self.
On the other hand, I think the Sage is wrong when he says that a spell is disqualified if "it
can target an object". Nowhere in the RAW it says something like that, it only says "targets only one creature" which is not about the spell in general but it's about a particular casting of that spell. In fact the RAW also says "To be eligible, a spell must be incapable of targeting more than one creature
at the spell’s current level" (which is once again to avoid lots of rolls if you Twinned a Magic Missile or Scorching Ray even directing all bolts the same creature). If you can Twin a 1st-level Charm Person because it doesn't matter that the spell can't be twinned when you cast it on multiple targets, then you can Twin a Dispel Magic cast on a creature because it doesn't matter that the spell can't be twinned when cast on an object. Unless they update the errata to "To be eligible, a spell must be incapable of targeting
an object or more than one creature
at the spell’s current level" the RAW allows to Twin a Dispel Magic or Remove Curse, as long as you cast it on a creature.
But generally speaking, I cannot think of any ineligible spell which would truly break the game if you allow it to be Twinned. Not a spell casting an object for example, but neither Fireball to be honest.
And I generally despise this design approach of adding spanners in the works just to
indirectly tone down a character ability, because a savvy gamer will always find enough particular spells which do qualify and will happily use Twinned Spell every round anyway. If they wanted to prevent this sort of abuse, they should have
directly prevented it, maybe putting a spell level limit or another usage limit.