"Women" don't do that – it's wrong to generalize in such broad terms.

It's true that people will use all kinds of psychological tricks to sway someone to their side in a conflict, and they use those tricks, that they generally feel are the most effective in a particular situation: Some try to wiggle themselves out of trouble by their speaking skills ("silver tongues"), others by intimidation, extortion, bribes, is extremely protective of and benevolent towards women and children, some women utilize this to gain something they want, e.g. "playing victim", because it compels others (especially men) into helping them immediately or being very gracious towards them.

As for "trying to gain equality": It's hard to assess someone else's true intentions, so it's hard to say if someone really is aiming for equality.

Mind the gap - is gender equality a reality in businesses today? -  Delta2020 | Financial and Technology Consultancy

If you mean feminists (instead of women), then yes, some of them use these tactics, though these are usually the ones who aren't interested in equality, but act like any other special interest lobby group. Unfortunately these kind of techniques, that some feminists employ, are quite normal in modern US / western politics: There is a lot of "spin", lying, hypocrisy, hyperbole, exaggeration, misleading, unethical, … stuff going on. You find that in pretty much every area of politics like environmental issues, Democrats/Republicans, social security, foreign policy/terrorism, …

The best thing one can do is to ignore all these people, since there is a huge tendency to always look at and portray the most extreme examples. Instead we should support those moderates, who stick to truth, the facts, and act decently – like the amazing Christina Hoff Sommers among contemporary feminists.