widersprechen
to contradict
To express a different opinion to a person and not agree with them. The verb is used with the dative.
Ich muss Ihnen da leider entschieden widersprechen.
I'm afraid I must strongly contradict you there.

to contradict
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to contradict
To express a different opinion to a person and not agree with them. The verb is used with the dative.
Ich muss Ihnen da leider entschieden widersprechen.
I'm afraid I must strongly contradict you there.

The verb is made up of 'wider' (against) and 'sprechen' (to speak). Its literal meaning is therefore 'to speak against.' It is an inseparable verb; the prefix is never separated from the stem.
Er hat nie widersprochen, wenn seine Eltern etwas entschieden haben.
He never contradicted his parents when they made a decision.
A very important point: 'widersprechen' (to contradict) always requires the dative. Whether you contradict a person, a statement, or an official notice, the object is in the dative.
Die neuen Fakten widersprechen der alten Theorie.
The new facts contradict the old theory.
When contradicting a person, this is often intensified or softened with adverbs. Typical combinations are 'entschieden widersprechen' (to strongly contradict), 'vehement widersprechen' (to vehemently contradict), or 'freundlich widersprechen' (to politely contradict).
Ich muss Ihnen da ganz entschieden widersprechen.
I must strongly contradict you there.
In this meaning, the subject and the dative object are often impersonal. It is about a logical conflict between two things, e.g. between actions and words or between two statements.
Dieses Ergebnis widerspricht allen Erwartungen.
This result contradicts all expectations.
This meaning belongs to official and legal language. Here, you object to an official document, for example a 'Bescheid' (official notice), a 'Mahnbescheid' (payment order), or a 'Rechnung' (invoice).
Wenn Sie der Rechnung widersprechen wollen, müssen Sie das schriftlich tun.
If you want to object to the invoice, you have to do it in writing.
against it / however
'dagegen' and 'widersprechen' can both express that someone does not agree. 'dagegen' describes the position more: you are against an idea or a plan. 'widersprechen' describes the verbal action more strongly: someone directly tells a person that they have a different opinion. In addition, 'widersprechen' can also mean that two statements do not fit together. Practical tip: 'dagegen sein' (to be against it) is an attitude; 'jemandem widersprechen' (to contradict someone) is usually a direct reaction in a conversation.

Sie widerspricht ihrem Chef, weil die Zahlen nicht stimmen.
She contradicts her boss because the numbers are incorrect.
Der Plan klingt gut, aber einige Kollegen sind dagegen.
The plan sounds good, but some colleagues are against it.