Plotly: Dropdown menu won't show plots

It's hard to tell what works and what doesn't in your code snippets since you've provided a datasample that just does not work. However, I do have a suggestion for you that answers your question directly regarding:

I am trying to plot three graphs (day, month, year) and give the user the option to pick which graph they want to see with a dropdown menu

The snippet below will let you chose between two datasets: year and month. And those are the exact datasets that you've provided. When you've got a working sample for days, that dataset can be easily included. And I'll happily do that for you when you're ready.

Anyway, the following plot will let you chose year and month using a dropdown menu. And don't worry if the design wrt line and marker style are not to your liking. That is simply included in the code as placeholders for you to change as you see fit.

Year

Month

DAY

(tba...)

Complete code

import plotly.graph_objects as go
import pandas as pd

df_y=pd.DataFrame({'x':[2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020],
                   'y':[  73,  562, 1153,  700, 2104, 1816, 1691, 1082,  914,  482]})

df_m=pd.DataFrame({'x':['2011-06', '2011-07', '2011-08', '2011-09', '2011-10', '2011-11',
                        '2011-12', '2012-01', '2012-02', '2012-03', '2012-04', '2012-05',
                        '2012-06', '2012-07', '2012-08', '2012-09', '2012-10', '2012-11',
                        '2012-12', '2013-01', '2013-02', '2013-03', '2013-04', '2013-05',
                        '2013-06', '2013-07', '2013-08', '2013-09', '2013-10', '2013-11',
                        '2013-12', '2014-01', '2014-02', '2014-03', '2014-04', '2014-05',
                        '2014-06', '2014-07', '2014-08', '2014-09', '2014-10', '2014-11',
                        '2014-12', '2015-01', '2015-02', '2015-03', '2015-04', '2015-05',
                        '2015-06', '2015-07', '2015-08', '2015-09', '2015-10', '2015-11',
                        '2015-12', '2016-01', '2016-02', '2016-03', '2016-04', '2016-05',
                        '2016-06', '2016-07', '2016-08', '2016-09', '2016-10', '2016-11',
                        '2016-12', '2017-01', '2017-02', '2017-03', '2017-04', '2017-05',
                        '2017-06', '2017-07', '2017-08', '2017-09', '2017-10', '2017-11',
                        '2017-12', '2018-01', '2018-02', '2018-03', '2018-04', '2018-05',
                        '2018-06', '2018-07', '2018-08', '2018-09', '2018-10', '2018-11',
                        '2018-12', '2019-01', '2019-02', '2019-03', '2019-04', '2019-05',
                        '2019-06', '2019-08', '2019-09', '2019-10', '2019-11', '2019-12',
                        '2020-01', '2020-02', '2020-03', '2020-04', '2020-05', '2020-06'],
                    'y':[  1,   1,   2,   8,   4,  20,  37,  79,  16,  13,   8,  12,   2,   5,
                         68, 139,  57,  64,  99, 182,  63,  60,  74, 128,  59, 109, 126,  86,
                         77, 112,  77,  78,  44,  32,  22,  33,  46,  61,  66, 109,  81,  78,
                         50, 140, 151, 297, 173, 225,  69, 119, 213, 177, 134, 217, 189, 255,
                        149, 114, 127, 154, 116, 110, 150, 184, 179, 117, 161,  48, 115, 147,
                        153, 199, 174, 195, 154, 162, 114, 140,  90, 156,  81, 107,  62,  64,
                         49, 128, 127,  60,  89, 115,  44,  58,  86,  65, 102,  93,  82,  78,
                        158,  65,  50,  77,  55,  71,  70, 105, 124,  57]})

# IMPROVEMENT 1
# INSERT ANOTHER DATAFRAME FOR DAYS HERE WITH THE SAME STRUCTURE AS ABOVE

# IMPROVEMENT 1
# INCLUDE THE DATAFRAME AS VALUE AND THE NAME df_d as key
# in the dict below:

dfc = {'year':df_y, 'month':df_m}

# set index
for df in dfc.keys():
    dfc[df].set_index('x', inplace=True)


# plotly start 
fig = go.Figure()
# menu setup    
updatemenu= []

# buttons for menu 1, names
buttons=[]

# plotly start 
fig = go.Figure()
# one trace for each column per dataframe: AI and RANDOM
for df in dfc.keys():
    fig.add_trace(go.Scatter(x=dfc[df].index,
                             y=dfc[df]['y'],
                             visible=True,
                             #marker=dict(size=12, line=dict(width=2)),
                             #marker_symbol = 'diamond',
                             name=df
                  )
             )


# some line settings for fun
lines = [dict(color='royalblue', width=2, dash='dot'), dict(color='firebrick', width=1, dash='dash')]
markers = [dict(size=12, line=dict(width=2)), dict(size=12, line=dict(width=2))]

# create traces for each color: 
# build argVals for buttons and create buttons
for i, df in enumerate(dfc.keys()):
    args_y = []
    args_x = []
    for col in dfc[df]:
        args_y.append(dfc[df][col].values)
        args_x.append(dfc[df].index)
    argVals = [ {'y':args_y, 'x':args_x,
                 'marker':markers[i], 'line': lines[i]}]

    buttons.append(dict(method='update',
                        label=df,
                        visible=True,
                        args=argVals))

updatemenu=[]
your_menu=dict()
updatemenu.append(your_menu)
updatemenu[0]['buttons']=buttons
updatemenu[0]['direction']='down'
updatemenu[0]['showactive']=True


fig.update_layout(showlegend=False, updatemenus=updatemenu)
fig.show()