The man isn't Jewish in this case, so he has no obligation whatsoever in marrying a Jewish woman. It is forbidden for the Jewish woman to marry this man because he is not a Jew. If the man truly feels a connection with Judaism he should convert.
Rashi on Shemot 10:22 writes regarding the plague of darkness
And why did He bring darkness upon them? Because there were wicked
people amongst the Israelites of that generation who had no desire to
leave Egypt, and these died during the three days of darkness so that
the Egyptians might not see their destruction and say, “These, (the
An Eishet yefat toar is not Jewish because there is no Kiddushin for her. Kiddushin 68b:
א"ק (דברים כא, יג) ואחר כן תבוא אליה ובעלתה וגו' מכלל דמעיקרא לא תפסי בה קידושין
Only After she has cut her hair let her nails grow and cried for her mother and father or avoda zara, then you are able to marry her and become her husband this implies that there is ...
Following @mbloch's sleuthing here, this seems to come from R. Yitzhak's Abravanel's comments on the passage Avadim Hayinu in his commentary Zevach Pesach to the Haggadah:
וכבר זכרו חכמים זכרונם לברכה שהיו עבדים נסגרים שם בכ״ד מפתחות שלא היה אפשר לצאת
Our Sages have already mentioned that slaves there [in Egypt] were confined with 24 keys, so that it ...
Where/when religion is in vogue, Jews are and have been hated ("nobly" once called "Judenhaas") for rejecting Jesus (or Mohammed). Where/when religion is passe, and "science" is the highest cause, Jews were "nobly" hated because of their "biological race" ("antisemitism").
Likewise, Jews have been (and still are) historically hated by the far right as "...
The Torah is (seemingly) explicit that all G-d's servants left Egypt (Exodus 12.41):
וַיְהִי מִקֵּץ שְׁלֹשִׁים שָׁנָה וְאַרְבַּע מֵאוֹת שָׁנָה וַיְהִי בְּעֶצֶם הַיּוֹם הַזֶּה
יָצְאוּ כָּל־צִבְאוֹת ה' מֵאֶרֶץ מִצְרָיִם׃
at the end of the four hundred and thirtieth year, to the very day, all the ranks of the LORD departed from the land of Egypt.
Aside from pointing you to specific halakhot in a piece like Shulhan `Arukh, I think the underlying philosophical difference (which significantly impacts one’s approach to Halakhah) is: if Judaism is strictly a religion than those who are lax about their Judaism are less Jewish perforce. But, if we are foremost a family, we continue loving one another ...
As you suggested in comments, R Yosef Deutsch quotes this in his book Let my nation go, p. 54, but he doesn't give details. He writes
There was no escape. The Egyptians had twenty-four different
safeguards against unauthorised flight. The Jewish people were so
deeply ensnared that they lost all hope of ever extricating themselves
by their own power. ...
I personally think the reason is explicitly presented in Avos 3,1:
"רַבִּי חֲנִינָא סְגַן הַכֹּהֲנִים אוֹמֵר, הֱוֵי מִתְפַּלֵּל בִּשְׁלוֹמָהּ שֶׁל מַלְכוּת,
שֶׁאִלְמָלֵא מוֹרָאָהּ, אִישׁ אֶת רֵעֵהוּ חַיִּים בְּלָעוֹ."
"Rabbi Chanina, the Deputy High Priest, says: Pray for the welfare of the government, for were it not for the fear of it, man would ...