
hineinziehen
to drag in
To involve someone against their will in an unpleasant situation, a conflict, or a problem.
Ich lasse mich nicht in euren Streit hineinziehen.
I won't let myself be dragged into your argument.
to drag in / pull in
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to drag in
To involve someone against their will in an unpleasant situation, a conflict, or a problem.
Ich lasse mich nicht in euren Streit hineinziehen.
I won't let myself be dragged into your argument.

to pull in
To move someone or something with force to a place or into something.
Er packte mich am Arm und zog mich in das laute Zimmer hinein.
He grabbed me by the arm and pulled me into the loud room.

to drag on
To extend or stretch out over a longer period of time. Often used for processes or events.
Die Verhandlungen zogen sich bis spät in die Nacht hinein.
The negotiations dragged on until late into the night.
'Hineinziehen' (to drag in / pull in) is a separable verb. The prefix 'hinein-' comes at the end in main clauses. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Er zog mich in die Diskussion hinein.
He dragged me into the discussion.
The verb consists of the directional element 'hinein' (into something) and the verb 'ziehen' (to pull). The literal meaning 'in etwas hineinziehen' (to pull into something) helps you also understand the figurative meaning 'in eine Situation verwickeln' (to involve in a situation).
Der Staubsauger hat eine kleine Münze hineingezogen.
The vacuum cleaner sucked in a small coin.
This figurative meaning often follows the pattern 'jemanden in etwas (Akkusativ) hineinziehen' (to drag someone into something). The 'etwas' (something) is usually an unpleasant situation such as an argument, a problem, or a conflict.
Versuch nicht, mich in deine Probleme hineinzuziehen.
Don't try to drag me into your problems.
In the meaning 'sich in die Länge ziehen' (to drag on), the verb is always used reflexively with 'sich'. The subject is usually a process, an event, or a period of time.
Das Projekt zog sich über mehrere Monate hinein.
The project dragged on over several months.
to include
Einbeziehen refers to neutral or intended participation in something. Hineinziehen, on the other hand, means that someone is involved against their will in a conflict or another unpleasant situation. Einbeziehen is used for voluntary participation, while hineinziehen is used for involuntary involvement.

Die Kollegen ziehen Lea gegen ihren Willen in den Streit hinein.
The colleagues are dragging Lea into the argument against her will.
Wir beziehen Lea auf ihren Wunsch in die Diskussion ein.
At Lea's request, we are including her in the discussion.