What the two elements do to each other
Fire acts on impulse and earth checks the ground first. In practice that means Aries has usually decided while Taurus is still examining the situation, and both experience the other as unreasonable about it.
The productive version is a division of labour: Aries supplies the initiative and Taurus supplies the follow-through, which is a combination that finishes things neither would finish alone. The unproductive version is Aries treating deliberation as obstruction and Taurus treating speed as recklessness, which is the same difference read uncharitably.
Cardinal against fixed
Modality matters more here than element. Aries is cardinal and starts; Taurus is fixed and holds. Neither modality is built for changing course, and that is where the friction concentrates.
Once Taurus has settled into an arrangement, argument does not move it and urgency does not move it. What moves Taurus is a change in the material facts. Aries, whose usual method is pressure, tends to discover this slowly and expensively.
Mars and Venus, which is the actual question
Aries is ruled by Mars and Taurus by Venus, so the pairing puts the two bodies most associated with attraction on either side of it. That is why the combination has the reputation it does.
Whether it plays out depends entirely on where those two planets actually sit in the two charts, which a sun sign cannot tell you. Mars in a slow sign softens an Aries considerably; Venus in an airy position loosens a Taurus. The form above answers this from the real positions.
Where it grinds
Pace, and the reading of pace. Aries experiences Taurus as immovable and Taurus experiences Aries as unable to sit still, and both descriptions are accurate.
The second friction is about ending things. Aries starts easily and abandons easily; Taurus is as hard to stop as it is to start. Arrangements that have clearly finished tend to continue for longer than either would choose alone.
What actually decides it
Not the sun signs. Two Aries and Taurus couples can have completely different comparisons depending on where the Moons, Venus and Mars fall, and the contacts between those four are what people describe when they describe a relationship.
A sun-sign pairing is a starting point that describes a tendency across a large population. The comparison of two actual charts describes the two people involved, and the difference between those two claims is the whole reason this page has a form on it.
Questions people ask about this
Is Aries and Taurus a good match?
The pairing has a real complementarity, initiative against follow-through, and a real friction about pace. Whether it works is decided by the rest of the two charts rather than by the sun signs.
Why does this pairing argue about the same thing repeatedly?
Because cardinal and fixed both resist changing course. Neither modality concedes easily, so a disagreement about timing recurs rather than resolving.
Does the Mars and Venus rulership mean strong attraction?
It means the two bodies associated with attraction are on either side of the pairing. Whether that produces anything depends on where Mars and Venus actually sit in the two charts.
Should I read anything besides sun signs?
Yes, and the Moon, Venus and Mars usually matter more. The form on this page shows all four for both people and the close contacts between them.