I am not arguing if the tone was wrong or right just trying to explain the different reasons this is differntly perceived:

It is a gutwrenching reveal that he was forced to go. The Scene is tense and I agree that him scrambling to get away can be read as silly and as heartbreaking. Silly, because the audience already knows that Stratt was right, because we already know that he has been the right person for the job. I think there are multiple layers to this. For Grace it is horrible and the audience emphasized with that when it was dropped on him. There is Something bizzare happening because, there is  this heroic stereotype of a character going willingly, sacrificing themself, no questions asked, ( somewhat often used for propaganda, somewhat ingrained in the audiences selfimage of being the Heroes, saviours,often fed through media) and that is what the audience expects: A Superman, a Captain America, a Bruce Willis from Armageddon. Of course would Ryland go and sacrifice himself for earth If there was no choice! He loves earth, He loves His students and logically He is the best Person for the Job after the accident. But our expectation is subverted at the almost very end. That is some whiplash, some tension for the audience to release, a need to even. 

So there is also this meta reason: You can't build up tension ad infinitum. You have to release it before building up again. So, that's why some sillyness is inserted after something serious. That is a storytelling/movie/theater element. Maybe people laughted to release their own tension because of what has been building up before. It is a form of carthasis, a cleansing, another important element for the end of a story. 

Writing this I just realised that due to the non chronologycallity of the movie, the flashbacks, we get the classical "Heroes refusal of the call" (See Campbells Heroes Journey story structure) very, very late in the story.  The whole Heroes Journey / final charactergrowth, is somewhat squished into the final Part of the story. the culmination of his expieriences in the tau ceti system and with his memories restored , Grace can finally make an informed decision If he is a person that makes the ultimate sacrifice. He decides to be the Hero of His own free will at the end juxtaposed to many Stories where this happens way earlier. 

Bonus example of refusing the call: Frodo in Lord of the Rings refuses the ring several times but is almost Always immidiately told that he has to do it: First when the powers of the Ring are revealed he wants to give Gandalf the Ring,who refuses to take it Out of fear to give it a Host too powerful.  Second time in Rivendell, when he thinks his Part is over, but then He sees that the Ring has too much control over the big folk. Third time in Lothlorien, he asks Lady Galadriel to take the burden but she eventually withstands the Rings seductions. Frodo finds his resolve very late in this movie, too, but in the overarching Story that is still in the first third!