Data source formula in Graph

as memory serves you cannot use INDIRECT for a Chart Data Range
i.e. even if you use via an intermediate (and fully qualified) named range, leveraging the INDIRECT, the Chart will still convert it to a fixed address.

others, e.g. Andy Pope, may be able to tell you otherwise - I am not a Chart whizz.

As an alternative, have you considered using a Pivot Table + Chart ? I don't think that has the same issues...

e.g. if in your file you put "Series" in A1 on both Jan & Feb sheets then, configure a Name:

Name: _Chart_Rng
RefersTo: =INDIRECT("'"&CHART!$I$3&"'!A1:D4")

you can then create the Pivot Chart using _Chart_Rng as the source (it will create the Table first, to which you can add the Chart via Analyze tab on the Ribbon [with Pivot active])

as you change I3 so your Pivot Table & Chart will update, once refreshed... you can, if desired, add a VBA Worksheet Change Event (for I3) to refresh the Pivot as and when the drop down is updated.

all of the above present in the attached.

Instead of a drop down list you could use a Table (not Pivot) + Slicer.
To use a Table you would need not use one sheet / month, but add all months to one sheet.

See attached file.