As a tech lead, it's actually easier for you to admit weaknesses, since your subordinates will be happy if you arrange things such that their job satisfaction is high, regardless of how much or little technical work you do. For a front-line engineer it's more dangerous, particularly if there is a perception (even if unfair) of a discrepancy between how they presented themselves at interview, and how they are presenting themselves now. Front-line engineers also don't necessarily know if their employer is thinking of firing them - they therefore are best advised to play it safe with regards to any little thing that their employer could pick up on as a straw that breaks the camel's back. Better safe than sorry.
But yes, there are times when we all need to ask for help, and even here, there are better and worse ways to do it. Again, for a team lead to express vulnerability can be positive in the right circumstances - because it can allow a junior (or indeed a senior) to puff up their chest with pride as they may then be able to help out their boss, show off their knowledge and look really good - and it can help to bond with the team. In contrast, showing vulnerability as a subordinate, to the wrong manager, can just give them an excuse to fire you. That's happened to me twice - I've learned my lesson.