It is known that Abraham forces Eliezer to swear him about finding Itzhak Shidduch. Why did he need to force him to swear. Let's assume that Eliezer would have brought the wrong Shidduch, Abraham and Itzhak could refuse to marry her or divorce her. Moreover, why didn't Abraham increase his search efforts by sending several emissaries (Shlichim) in parallel in order to find the appropriate Shidduch?
Let us first begin by quoting the pasuk in Bereishis 24:2-4 for context:
וַיֹּ֣אמֶר אַבְרָהָ֗ם אֶל־עַבְדּוֹ֙ זְקַ֣ן בֵּית֔וֹ הַמֹּשֵׁ֖ל בְּכָל־אֲשֶׁר־ל֑וֹ שִֽׂים־נָ֥א יָדְךָ֖ תַּ֥חַת יְרֵכִֽי׃וְאַשְׁבִּ֣יעֲךָ֔ בַּֽה' אֱלֹקי הַשָּׁמַ֔יִם וֵֽאלֹקי הָאָ֑רֶץ אֲשֶׁ֨ר לֹֽא־תִקַּ֤ח אִשָּׁה֙ לִבְנִ֔י מִבְּנוֹת֙ הַֽכְּנַעֲנִ֔י אֲשֶׁ֥ר אָנֹכִ֖י יוֹשֵׁ֥ב בְּקִרְבּֽוֹ׃ כִּ֧י אֶל־אַרְצִ֛י וְאֶל־מוֹלַדְתִּ֖י תֵּלֵ֑ךְ וְלָקַחְתָּ֥ אִשָּׁ֖ה לִבְנִ֥י לְיִצְחָֽק׃
And Avraham said to the senior servant of his household, who had charge of all that he owned, “Put your hand under my thigh: And I will make you swear by the LORD, the G-d of heaven and the G-d of the earth, that you will not take a wife for my son from the daughters of the Canaanites among whom I dwell: But will go to the land of my birth and get a wife for my son Isaac.”
According to Ramban the oath served a two-fold job. Firstly it clearly concretised Avraham's wishes and thereby legacy, that if he were to die with Yitzchak still unmarried these wishes would be carried out, and secondly, Eliezer could well have been the trustee for Avraham's estate, so he commanded him to have Isaac marry specifically according to his wishes so that that he should make Yitzchak's inheritance of his estate contingent on this condition.
The act of getting Eliezer to swear was to make it crystal clear that if Eliezer were to disobey this command he had to be weary of "אֱלֹקי הַשָּׁמַ֔יִם וֵֽאלֹקי הָאָ֑רֶץ" - i.e. that there is a higher source that would find him accountable.
By getting Eliezer to swear he was ensuring that no future generations would questions the 'yichus' - the lineage of the Jewish people. "Avraham did not want that in the future anyone could claim that his claim on the Holy Land was based on intermarriage with the previous owners of that land. It had to be established beyond any shadow of a doubt that the Israelites’ claim to the land was based on G-d having promised it to their founding father, and that He used His Power to do this on their behalf." (Sefaria translation)
According to the Malbim, Avraham made Eliezer swear as the daughters of Canaan had such bad, destructive middos (character traits) it would negatively impact on Yitzchak and leave a lasting impression and therefore Avraham had to ensure this didn't happen.