I have been trying to get into Startups at Director / Sr.Director level and most of the times all the 5-8 interviews are mostly concentrated on Technical side. Even if a round is to guage People management , the interviewers spend the first 40-50 mins on technical side and leave the remaining 10 mins for people management.  These roles are in India with either local or US based startups.All the feedback i get is that my people management skills are not where they would like it to be. 
I am already managing teams and managers under me for the past 4 years now.There are different set of two questions that i get asked and mostly i have seen one of them being: 
* have you had to let go under performers and what was that like and the process there?  I have had this situation a couple of times now, however the way i handled it was following the policy of the current company, where in before officially working on PIP (Performance improvement plan) with HR involved,I work with the member to let them know that we dont see delivery from them at expected levels and would love to understand if they need additional walk through on any of the technical items, or if there are any personal issue that is causing a drop in their performance and if there is way i can help or if they are getting help, or they would like to discuss it with someone etc. Based on what i hear the next plan is provide them all help i can give them and if performance still does not meet expected levels then we work on a dedicated PIP plan with tasks identified for the next 2-4 weeks time frame with close monitoring. In the meanwhile i also work with HR to see if there other teams not having as high bar for technical candidates and would they be willing to give this candidate a chance etc. The candidate did not perform yet and hence was asked to look out since we could not find another team interested as well ( can understand the reluctance of others ).However I am not sure if there are major gaps in the way this was handled or if startups are looking for some different answers like immediately fire them or are there radically different mechanics of working this out since looks like this shows them such a big gap on people management side that they decide to drop me.Any experiences or advice would help, thanks !