You are on the right track, Gabriel. Often with Binomial models, what we want to compare is the ratio of the odds of survival. In this case, between males and females on the ship. Their expected odds of survival has the form:

For two individuals i and j, the ratio of the expected odds is:

Notice that the odds ratio depends only on the difference between the values of the corresponding regression variables such as Age, Sex and Pclass. For indicator variables such as Age, the difference (x_i-x_j) is always 1. If Sex is encoded as follows: Male=126 and Female=125, the ratio of odds w.r.t. Sex is:

On the Titanic, β_sex happens to be -2.6526. So the odd ratio is e^( -2.6526) = 0.07047. Thus, odds of survival for males on the Titanic was 7% of that of females.

Another place you will see this situation is with the hazards ratio in Survival Analysis.

I hope it’s clear now. I see that you are thinking about this topic in the right sort of way as your questions are insightful.

‘best