Mutable squares do not deadlock, they drift
The interesting thing about the Gemini difficulty list is that every sign on it is mutable, as Gemini is. Mutable signs end their seasons and are built to adapt, so a hard angle between two of them does not produce the immovable standoff that fixed signs manage. It produces something else: both parties adjust, repeatedly, and the underlying question is never put.
That is a genuine failure mode and it is not what the word worst suggests. Nothing breaks. It simply never settles.
Mercury against Jupiter
Gemini belongs to Mercury and Sagittarius to Jupiter, and the opposition between them is the old contrast between detail and scope. Mercury gathers particulars and declines to generalise; Jupiter reaches a conclusion and finds the particulars tiresome. Virgo, also a Mercury sign, squares Gemini from the earth side, and Pisces, classically a Jupiter sign, squares it from water.
So the whole Gemini difficulty list is two planets arranged four ways. Once that is visible, the sensible question is where Mercury and Jupiter actually sit in the two charts, which has nothing to do with either sun sign.
The opposition is a division of subject
Two signs at 180 degrees hold the ends of a single axis and share a mode. Gemini and Sagittarius both concern knowledge: how it is gathered and what it is for. Each has half the problem, and partnerships across an axis are common precisely because the halves fit.
Whether that is experienced as completion or as being permanently corrected is not something an angle decides.
What the lists cannot see
A square is 90 degrees between signs of the same mode and incompatible elements, and the classical term for it is hard rather than bad: friction that forces movement. Its severity depends on how exact it is, and two sun signs give no information about that. A Gemini sun at two degrees and a Virgo sun at twenty-seven are twenty-five degrees off a true square and a comparison would not count the aspect at all.
What does show up reliably is Saturn from one chart on the other's Moon or Venus, felt as coldness; Neptune on a personal planet, felt as confusion; and hard Mars contacts, which describe how quickly a disagreement gets loud. The synastry calculator measures the actual angles from two birth times, and synastry describes what the method looks at.
A pair page says more
Gemini and Pisces has its own entry setting out what the two do easily, where they lose each other and what two mutable signs do when neither will state a position. That is information; a ranking is not.
Where both birth times exist, compare the charts and stop guessing from birthdays.
Questions people ask about this
Which signs are hard angles for Gemini?
Sagittarius opposite, Virgo and Pisces square. All three share Gemini's mutable mode.
Is Sagittarius a bad match for Gemini?
Not by the angle. The two hold opposite ends of one axis and the tradition reads that as attraction as often as conflict.
What is different about mutable friction?
It tends to drift rather than deadlock: both parties adapt and the underlying question is never settled.
What actually indicates a hard pairing?
Saturn or Neptune on the other person's personal planets, close Mars contacts, and how exact the aspects are.