
unfähig
unable
Not having the necessary ability, competence, or strength to do something specific or meet a requirement.
Nach dem Unfall war er unfähig, seinen Arm zu bewegen.
After the accident, he was unable to move his arm.
unable
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unable
Not having the necessary ability, competence, or strength to do something specific or meet a requirement.
Nach dem Unfall war er unfähig, seinen Arm zu bewegen.
After the accident, he was unable to move his arm.

incapable of
In a fixed expression, used to express that someone is emotionally or character-wise not capable of showing a particular feeling or behavior.
Er scheint unfähig zu echter Reue zu sein.
He seems to be incapable of genuine remorse.
The adjective 'unfähig' (unable) is the direct opposite of 'fähig' (able/capable). The prefix 'un-' is often used in German to negate the meaning of adjectives and nouns.
Er fühlte sich nach der Operation noch unfähig zu arbeiten.
After the operation, he still felt unable to work.
'Unfähig' (unable/incapable) is often used in two ways: followed by an infinitive with 'zu' (to) to describe an action, or followed by 'zu' + noun to describe an emotional or character trait.
Er war so müde, dass er unfähig war, einen klaren Gedanken zu fassen.
He was so tired that he was unable to form a clear thought.
In the meaning 'not capable in terms of character,' 'unfähig' (incapable) is often combined with abstract nouns that describe feelings or social behaviors. Typical examples are 'unfähig zu Mitgefühl' (incapable of compassion), 'unfähig zur Liebe' (incapable of love), or 'unfähig zur Empathie' (incapable of empathy).
Sein Verhalten zeigt, dass er unfähig zu jeder Form von Selbstkritik ist.
His behavior shows that he is incapable of any form of self-criticism.
unsuitable
Unfähig emphasizes that someone cannot do something or does not meet a specific requirement. Ungeeignet gives a more general assessment of whether a person is a good fit for a position or task; a lack of ability can be one reason. Use unfähig for actual ability and ungeeignet for overall suitability.

Er ist unfähig, die Maschine ohne Hilfe sicher zu bedienen.
He is unable to operate the machine safely without help.
Er ist für die Stelle ungeeignet, weil sie regelmäßige Nachtschichten verlangt.
He is unsuitable for the position because it requires regular night shifts.