May a person who was asked to be the Baal Korei refuse to do so?
One who is offered to read the Torah and refuses to read it, his days are shortened.[1] One is thus not to refuse being the Baal Korei once he has been [publicly[2]] called up.[3] [If, however, he was privately asked to read the Torah he may refuse.]

Justifiable reasons for refusal:[4] The above prohibition only applies if there is no justifiable reason for refusing the Aliyah. If, however, there is a justifiable reason for why he does not want the Aliyah then it may be refused.[5] For example, if he did not review the Parsha two or three times beforehand, he is not to read it and may refuse.[6] Or, he does not know how to read it properly.[7]

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[1] Brachos 55a, brought in M”A 53/22; Elya Raba 139/2; Peri Chadash 139/1; P”M 53 A”A 22; Levushei Serud 138; Lev Chaim 3/12 [See there that one time a person was called to the Torah and he ran out and he was later burnt to death within 30 days, as the Torah is called fire]; Toras Chaim Sofer 139/1; Aruch Hashulchan 139/4; M”B 139/1; Kaf Hachaim 139/3; 428/40; Tzitz Eliezer 14/34; It is however omitted from the Rambam, Tur and Michaber/Rama [see Elya Raba and Toras Chaim Sofer ibid for explanations of this omission] See also Levush 428 and M”B 428/19 who omit this

The reason: As the Torah is called our life, and one who refuses it is refusing life. [Brachos ibid]

[2] See Chaim Sheol 1/13 the Sefaradim are accustomed not to call up by name, but rather privately ask the person to go up, as if one is called up publicly and refuses his life is shortened.

[3] Although one all the Poskim who discuss this matter refer to a case of an Aliyah [and back then the Olah would then read the Torah], nevertheless seemingly it would all the more so apply today to the Baal Korei.

[4] Torah Leshma 95 and 428; See Tzitz Eliezer 14/34; Piskeiy Teshuvos 139/1

[5] The reason: As the danger is only when the person is belittling the Torah, as it is not important in his eyes, however when he does so for a justifiable reason he does not belittle the Torah. [ibid]

[6] Michaber 139/1; M”B 139/1; Kaf Hachaim 139/3

[7] Torah Leshma 95 regarding Maftir