Tosafot on Avodah Zarah 7a: [translation from here]
It is forbidden to ask [a second rabbi for permission] only if one does not inform him [that a first rabbi was consulted and he forbade it]... But certainly the [second] sage should be careful not to permit [what the first sage forbade], as we say in the chapter Kol Hayad [in Maseches Niddah], "A sage who forbade - his fellow is not allowed to permit unless he can respond to him, for instance if he made a mistake regarding a Mishnah, or even with equal logic."
(1) What is the point of allowing you to consult a second rabbi if that second rabbi is strongly discouraged from disagreeing with the first? Why not just say, "You must go with the first ruling you got."?
(2) Why should that second rabbi be asked to produce strong and convincing logical arguments for his disagreement, when the first rabbi is not also asked to produce equally strong and convincing logical arguments for his ruling in the first place?
(Note that Tosafot talk only about a case when the first rabbi "forbade"; because if the first rabbi permitted, very few Jews would ask for a second opinion!)
Note also that when you ask for a medical second opinion, no one is leaning on the second physician to agree with the first.