Don’t Waste Your 20s at Google or McKinsey
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Today, big banks/corporates/consulting firms now no longer offer that same social contract (they would argue they do, but they don't - with few exceptions). You are expendable and most firms would be happy for you to stay where you are (same role, same salary) and if you want to change, go find it outside the company.
So in complete agreement with the author that a big name brand name won't necessarily move your career forward.
But extrapolating that further, what I am now seeing is that this first choice can irreparably hamper your choices down the road. Following the 'traditional' and 'secure' path of a big company/consulting firm etc is now seen as the safe, risk free, dare I say boring choice. If you have any intention of being in a risky role (ie startup/entrepreneur) the signalling from a big comfortable riskless name on your resume may do more harm than good.
I review candidates for roles in a fast paced tech startup. If I have a choice between someone from say Microsoft and someone from a failed startup, everything else being equal, I will pick the startup man/woman every time.