To me, security in marriage, or in a romantic relationship in general, is about trust. There are no guarantees in life, but security in a relationship should be as close to one as possible. You should be able to be confident that your partner will not cheat, lie, intentionally harm you physically/emotionally/mentally, run your finances into the ground, etc.
Some of that comes from them, and some from you. They must show you that they can be trusted, but you also must be secure and confident enough in yourself to see that they are showing you that.
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