to acknowledge
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to not want to acknowledge
To refuse to accept an unpleasant or shocking fact as real.
Sie wollte es einfach nicht wahrhaben, dass sie die Prüfung nicht bestanden hatte.
She simply did not want to acknowledge that she had failed the exam.
The verb is made up of 'wahr' (true) and 'haben' (to have) and is separable. The prefix 'wahr' comes at the end in a main clause, but stays attached to the verb in a subordinate clause.
Er wollte die schlechte Nachricht nicht wahrhaben.
He did not want to acknowledge the bad news.
This verb is used almost exclusively in the fixed expression 'etwas nicht wahrhaben wollen' (to not want to acknowledge something). The 'etwas' can be a noun in the accusative or a whole subordinate clause with 'dass' (that).
Sie will seinen Verrat einfach nicht wahrhaben.
She simply does not want to acknowledge his betrayal.
The positive form, meaning the use without 'nicht' (not) and 'wollen' (to want), is extremely rare. It sounds very formal, almost old-fashioned, and practically does not occur in everyday speech.
Er musste die Niederlage als Tatsache wahrhaben.
He had to acknowledge the defeat as a fact.
to accept
'akzeptieren' and 'wahrhaben' both have to do with acknowledging a truth. 'akzeptieren' can be used for many facts, rules, or unavoidable situations. 'wahrhaben' refers especially to facts that are unpleasant, sad, or shocking. The form 'nicht wahrhaben wollen' is very typical: someone inwardly refuses to see a reality. Learners may confuse the words because both can mean 'to accept as true'. In practice: for an ordinary fact, you usually say 'akzeptieren'; for a painful truth and inner resistance, 'wahrhaben' fits better.
Am Abend will sie nicht wahrhaben, dass sie die Prüfung nicht bestanden hat.
That evening, she does not want to acknowledge that she did not pass the exam.
Nach dem Gespräch akzeptiert Max, dass der Kurs schon voll ist.
After the conversation, Max accepts that the course is already full.